I searched through to see if I could find any that haven't been mentioned yet (there's a lot). Mostly my answers all relate to one of the most expensive things people owned at the time: clothing.

Innovations in clothing production actually had a huge impact on society because it changed farming from being an inefficient, communal, subsistence-based practice, to a profitable, merit-based system, which lowered the amount of farmers and resulted in more people doing other stuff.

The Treadle Spinning Wheel

Spinning at that time was a slow and arduous process. The great wheel was considered a huge improvement, and the treadle spinning wheel is many times faster.

The Shuttle Loom

No longer will your people have to manually move the weft threads between the warp threads. Now they press a peddle to move the warp, and a shuttle carries the weft thread across.

The Carding Machine

Instead of manually combing your wool to get out the chaff and straighten out the fibers, you can just turn a crank and do a bunch at the same time.

And most importantly:

The Enclosure Movement

Just find the best farmers and put them in charge of the land. They will get profits from using the land more efficiently and getting higher returns. Maybe they will raise more sheep. Anyway, people work better when they have a stake in the results.

The enclosure movement will result in people moving from farms to cities. Before they can find jobs, a lot of people will starve to death, but after that, they will be making pretty much everything other than food which we have in society today.

The map of the world

The discovery of the world was very much incomplete from a European perspective in the 5th century. However any ordinary modern person has a much better grasp of how the world map is laid out.

John could sell the idea of exploring new (and rich) lands. If he could fund an expedition, the rest is alternate history.

I'm going to take the crazy approach and try for something new: polycarbonate and/or epoxy.

Just think for a second. Transparent fairly light shields that wont budge with a direct crossbow or war bow impact that could shatter an iron shield. Seafaring ships inmune to sea worms. Lightweight vehicles and structures that needs less horse power to move the same cargo. The sky is the limit!

The Toothbrush

According to Wikipedia:

The first bristle toothbrush resembling the modern one was found in China. Used during the Tang Dynasty (619–907), it consisted of hog bristles.

So, if John introduced it to Europe a couple hundred years earlier (and got people to believe it would help them live longer and actually use it), it might change things significantly.

John needs to invent the sulphur match. We can presume he has done some chemistry at high school and that he played with matches as a child. Maybe a small known fact is stuck in his head, and he knows enough to begin experimenting. According to Wikipedia, John's invention would anticipate the real thing by less than a hundred years, the first mass-produced match began in England around the 1840s.

A note in the text Cho Keng Lu, written in 1366, describes a sulfur match, small sticks of pinewood impregnated with sulfur, used in China by "impoverished court ladies" in AD 577 during the conquest of Northern Qi.[5] During the Five Dynasties and Ten Kingdoms (AD 907–960), a book called the Records of the Unworldly and the Strange written by Chinese author Tao Gu in about 950 stated:

If there occurs an emergency at night it may take some time to make a light to light a lamp. But an ingenious man devised the system of impregnating little sticks of pinewood with sulfur and storing them ready for use. At the slightest touch of fire, they burst into flame. One gets a little flame like an ear of corn. This marvelous thing was formerly called a "light-bringing slave", but afterward when it became an article of commerce its name was changed to 'fire inch-stick'.

Further information: https://medium.com/study-of-history/a-short-history-c52a80c69d5e

The wheelbarrow.

This is simple enough that John can understand it and build one using available tools without much enhancement.

It seems like wheelbarrows should always have existed, because they're so obvious - but the ancient Romans didn't have them. (They were invented in China in ~ 200 AD but didn't make it to Europe until the 13th century.) But once you see one and use one, their utility is obvious. They have a dramatic impact on small project agricultural and construction productivity, relative to the capital investment required to create one.

Raising these two types of productivity at such an early date will dramatically change history as a whole.

The Rocket Stove

Just a few slight modifcations to a traditional brick/steel/clay stove (not needing any additional materials, just a modified shape) drastically increases the burning temperature and fuel efficiency of a stove.

One of the things that held back development is the difficulty of smelting and metal working, the effective cost and difficulty of cooking, the expense of fuel, and much more.

A Rocket Stove, invented in the 1900's, is pretty much an amusing sidenote of technology today since we have more high-tech solutions of improving our fires such as electric blowers, bellows, space heaters, electric coils, blast furnaces, etc.

The rocket stove, had it been invented anytime between 4000 B.C. and 1700 A.D. (the whole range of which had the prerequisite technology), would have drastically revolutionized technological advancement.

Globalism... well kind of

Your best bet would probably not be any singular tool or idea but the knowlede of where to find more knowledge.

John remebers that different countries had different ideas at any given time, even though he doesn't exactly know who had what. But his greatest strenght would be that he has a LOT of hindsight.

Some examples:

• Where others see "a black powder that burns quick and stinks" he sees guns, dynamite and so much more.

• Where others see just a horse collar, he thinks of quick carriages, drawn by eight horses (eg. post coaches).

• He knows what lenses, maths, paper and so much more really are capable of beyond their obvious applications

He knows what is possible and the amount of ideas and concepts he has, that are already proven to work, is unrivaled. Most of these may not be doable in that era, but he can already make huge steps in the right direction (or make other people make huge steps) just by spreading this knowledge and nudging people in the right direction.
Plus he knows how important it is to properly document each step and make frequent backups of that documentation (especially for the black powder reasearch groups).

And even if none of these could possibly be expected to work during his lifetime, he DOES know how countries would benfit from the already existing inventions of other countries.

If he is rather attentive, he can travel one country to get a hold of their common knowledge and then travel further to countries like China or Arabia to get a good look at their current level. This might come with huge hurdles, as he would be considered a foreigner in any country and might not get easy access to their knowledge.

If he plays it right though, he might end up with some good connections to any country he visits, maybe even with the opportunity to send some bright minds over to learn anything he deems useful with his knowledge of modern times.
He would essentially establish the first global corporation ever.

How though?

He might be able to identify himself as some sort of travelling scholar.
If he is a foreigner anyway, he might as well be a reputable foreigner.
This might actually grant him some boons like becoming the guest of some wealthy people and getting their attention for a little while, which enables him to make connections and find investors/trading partners early on (or at least have a safe place to sleep and eat for a night or three).
Plus a scholar would of course seek knowledge. Nothing suspicious about that.

This way he can get access to the most promising ideas and inventions from all over the world (or their prototypes anyway) and start spreading them everywhere to make a huge profit off of them.

This way you pretty much get all the inventions mentioned here at once.
And all of this is possible with "just" entrepreneurship and soft skills. No previous research required.

Cutlery and plates?

Spoons, forks and plates are pretty basic and we use them every single day but nobody thinks "That spoon! I like that spoon! That spoon is great! What would I do without that spoon?"

Nobody really appreciates forks, spoons, plates and how important that simple stuff is, because it's something so simple and basic that we think that it's a totally normal everday tool. People ate back then with their hands and put their food on bread cause they didn't had plates and cutlery. Putting a fork in your meat and having clean hands after eating would change a lot. And now imagine how much money you can make with that invention. Change their lifes and throw a spoon in society!

Better agricultural practices

By introducing better plow technology like mouldboard plows and introducing techniques like crop rotation, you can start the agricultural revolution 1000 years earlier. This means a drastic increase in the yield of farmland, which allows to sustain a higher population density with less labor bound to food production. So you have a lot more labor available for all kinds of economic branches... or if you are more cynical, more disposable manpower to send into wars.

None.

There is common misconception that history is linear and things get invented and change the world. It's false.

Things get invented, then they fall into obscurity and get reinvented anew. Sometimes they even get forgotten after a period of widespread success, like phalanx formation.

John needs the same thing as Beth from 2348 who traveled to today with knowledge how to beat COVID-19 in 3 simple steps: being trusted by powerful and rich people who can make it happen. The thing that an outsider, like a time traveler, can never have.

John can't change the ancient world, just like Beth can't stop what's going to happen in early 2021.

The talent of John is to make people do things for him.

That's great! Instead of making a part which is then quickly copied, he should introduce some process. Processes normally need to be controlled, that's John's part, and they are less easy to copy from mere observation. Finally, you can cut a process in single task slices so that even the involved never learn all of it.

That can be mass production of a part (arrows?), modern organization of a restaurant, shoe making, what you want.

The key is, as a business man, he can then kick the concurrence off the market by being cheaper and higher quality at the same time.

Being a leader and business man he will certainly be fully capable of dealing with the mafia-like reactions and consequences that were normal at the times.

You're setting John into a quite violent time there!

John is a businessman after all. He might have no scientific skills, so inventing things which also require deep knowledge about chemical/physical processes would not fit his role. Unfortunately it also requires a lot of time and money. There is a lot of trial and error involved. Since neither John nor the blacksmith know how to make new alloys or invent things so that they work, it is not worth the try. In addition, who says that those new invention will sell like crazy and bring him a fortune? Not every inventor got rich within in his lifetime. Often inventions need time to get accepted - and this is even more true the further you go back in time. And more time is needed to 'sell' them to people. Further, you need either a rich patron to pay for the investments or already have some money.

So it is too risky and I propose another business method. John should not invent tools, produce them or try to sell 'new' technology. Instead, he should 'invent' what he knows best, e.g.:

Stock market

John knows about stocks and how a stock market works in principle. He is also affine with numbers. It is easy for him to evaluate the value of a business (e.g. the local blacksmith) and to calculate the share value. With some money from the priests, leaders or a wealthy trader, he can build up the first stock exchange.

Arabic numerals

The [insert whatever numerals are used in your location] are very inconvenient for book keeping and the stock market idea. So John invents the arabic numerals, which he uses every day. This will revolutionize not only mathematics, but will speed up accounting.

Banking - deposition and withdrawal system

The first prototype banks were invented around 2000 BC in Assyria, India and Sumeria. So he could also invent new things related to banking, which are not known at this time. Likely it is the deposition and withdrawal system - IMHO its early system was invented by the Templars in the 12th century. With this idea he could increase the safety of merchants and trading routes.

Marketing

John could earn some money making extensive advertisements for local businesses. He could design wall posters or invent logos printed on coins. Let him invent the basics of trademarks. So only local businesses are allowed to sell 'special' papyri or bricks, all marked with their logo.

Job market

You need skilled people for a certain job? John can help. He can establish a sort of recruiting service in every bigger city. With the 'invention' of CVs and resumes John can always find the best person.

Insurances

Everybody needs them. Together with a good marketing strategy John could establish a big insurance company. However, it needs a lot of risk management/analysis and I'm not sure if John knows how to handle that.

Homeopathy?

I'm not a fan of it, but John might be. Let him 'invent' a potion which heals every known disease. Paired with his business skills he knows how to market it. He can 'print' advertisements or bribe people to spread the word that this potion can heal everything.

First, may I just say that, in your story, John not being the type of person to prepare at ALL for his trip back in time makes absolutely no sense. If John is at least smart enough to have been able to make enough money to afford time travel, he should be smart enough to figure out what it is he is going to "invent" before going back if his entire reason for going back is to "invent" something. Someone who's fully-formed skills are "making money, influencing people, spotting gaps in the market, organising teams to do the things he doesn't have the expertise for, etc." is NOT going to go back in time with the sole purpose of "inventing" something that is already around in his own time and not HAVE THAT THING IN MIND. If John were truly that STUPID, he would probably already be dead.
That being said, with the limitations of John not being allowed to prepare at all and considering his skill set, my answer to you is:

John should "invent" the idea of fractional reserve banking, where one only keeps a fraction of the deposits available in order to loan the rest out and make money on the interest charged on those loans. With his skills of organizing people to do what he cannot coupled with his sole knowledge/expertise being economics learned "from the street", this should suit him to a tea.

Penicillin

There's a good chance that our hero has read about the accidental discovery of penicillin in a high school textbook. Given this, it shouldn't be hard to recreate the experiment, even with very primitive cooking utensils. You need some kind of jelly that's good for cultivating bacteria, a source of bacteria, and a little speck of mold.

You have to be lucky enough to find mold that contains the penicillium organism, and it may take a few tries before you succeed. After that, you need to learn how to cultivate penicillium and how to to purify penicillin, at least to some degree. It doesn't have to be anywhere near the standards for today's drugs.

Penicillin is a powerful weapon against many diseases caused by bacteria. Once the people have begun using penicillin against disease, they will never go back to the way they were before.

The invention that would have The most impact if John could get it accepted would be 3 field crop rotation. A 50% increase in farm output would be huge. Persuading farmers to change their ways would be a tough sell though.

The Instant Legolas!

Joerg Sprave did a lot to try to prove how simple a magazine system (and even a draw assist) can be. It's a bit of complex wood/metal work, but not outside the ability of a hand craft tools. Check out his videos he made as he developed the design.

One of the reasons people moved to crossbows and guns is because they're easier to make and easier to train soldiers to use - but they were often poor replacements to a truly well trained bowman. Joerg's invention let's a bowman hold their draw almost effortlessly, he even later strapped a second bow to the front of it as a draw assist desvice to make pulling a heavy bow easier without effecting the strength of the bow.

There's another video of someone who made one with hand tools and then let someone who actually shoots heavy bows try it. There was a learning curve, but apparently they thought with some extra time to practice with it it could have made shooting very easy.

Semaphore and/or Telegraph

Whatever time you are in, military technology and faster communication are always good.

When the Spanish Armada attacked England in 1588, the best system the English had to warn of the attack was to light a series of preconstructed bonfires - faster than a horserider, but a pretty crude (yes/no) message. Land semaphore was invented in 1792 in France and enabled more complex messages to be sent for military and other purposes. Signalling between ships with hand flag semaphore was common up to world war 2.

Needle telegraph is also not beyond what could be achieved with 5th century materials. A battery could be constructed from any two dissimilar metals (iron, and copper or lead) and any available mineral or organic acid (vinegar, rancid wine) with sufficient power to deflect a magnetic needle. The issue would be finding enough metal to make wires with. Here's a video on how to make a telegraph (with modern materials) in 6 minutes https://www.youtube.com/watch?v=1r2eOpkBTOo

Well, here's two things I can think of off the top of my head.

Germ Theory and Sanitation

The Germ Theory was truly groundbreaking when it first came out. Before bacteriological causes, every disease was assumed to be caused by either poison or an angry deity. As a result, most "cures" were ineffective, if not harmful (Pliny recommended eating the offending dog's head as a cure fore Rabies). Furthermore, they did almost nothing in the way of sanitation. As a result, introducing the Germ Theory, along with some basic sanitation techniques, would save many lives. Indeed, the "basic sanitation techniques" part probably wouldn't even be necessary - they knew "basic sanitation techniques" in the 5th century (have you ever read Leviticus?), they just didn't use them.

Modern Mathematical Notation

The ancients were really good at math (many of the theorems and equations you learn in Algebra and PreCalc predate the 5th century). However, actually doing the math was a pain, and transferring that knowledge to others was expensive due to the verbosity of their notation. The introduction of modern mathematical notation (Arabic numerals and arithmetic operators being the most important) would make math much easier. While "John" probably couldn't use this to make much money*, it could probably get him into a monastery (which were just starting to become rich during that period).

* EDIT: On second thought, tutors were paid huge sums back then - it wasn't every day that you could find someone who was both literate and looking for a job.

I'm going give you a frame challenge here. The fact that John has what I would consider sub-par levels of knowledge of modern technology means he's not really likely to be able to 'invent' anything with earth-shattering ramifications that didn't already exist and just wasn't seen for how useful it was at the time (see steam engines and hot air balloons as canonical examples of this, both were invented in antiquity but neither was recognized for it's utility until early modern history).

Let's put this in a slightly different context. How likely is it that a high-school dropout could explain to you how to make something like a mould-board plough? That's about as simple and useful as you can get for tools that hadn't been invented yet (and, were I setting out on a mission like this myself, is actually what I would pick, though I would likely also make the effort to get people to realize that the aeolipile was actually useful rather than just a curiosity) but it's not something almost anybody in modern times who hasn't actually used or made one is likely to be able to tell you how to make. Most other truly 'simple' tools that hadn't been invented yet hadn't been invented because there was no use for them. There's no need for a screwdriver if you don't have screws for example.

Essentially, your issue here is that he doesn't have enough knowledge to 'invent' physical tools. In fact, even less tangible stuff like modern business management techniques wouldn't have worked back then (because there just wasn't the population to support it effectively). Based on this, I contend that there is nothing he can do other than point out utility of inventions that have already been made but are not seen for how useful they are.

Cowlinator mentions it but it seems it didn't get much attention. Pasteurization is no small thing to invent!

For some strange reason, John can maintain milk for longer than other residents, his milk just won't spoil in a couple of days. There is no need to make perfect, standardized Pasteurization. John remembers from school that pasteurization entails heating. Amateurish low-heat warming can definitely get John a couple more days worth of milk. Assuming John has absolutely no idea, I can imagine him practicing by warming his milk for half an hour every day, practicing with the heat levels to avoid boiling it, maybe even wasting much milk in the process.

However, as noted in other answers and comments, what is no more important than how, of course. By setting up some apparatus, mainly for show, to attract the attention, John can definitely start offering to preserve the milk of neighbors. See, everybody observes that John buys more milk than others, while he is rarely seen throwing it away.

Little by little, John can perfect the "machinery" (which is simply used to slowly warm milk, of course) et voila! John is the alchemist du-jour, as milk really lasts somewhat longer after he has it flow through his machine. So, John has "invented" a tool that can be used to preserve milk.

EDIT

As Nosajimiki notes in a comment, obviously, even pasteurized milk only lasts a couple of hours at room temperature, unless it's quite cold... Unfortunately, John needs to remember that this is most effective in winter times. But as John's profits go up the first winter, he thinks there must be a way to make money during summers too. With time, he concocts a sort of a dripping machine, letting milk drip slowly through a hot furnace-like space. Droplets pass through the heat, drying up, with only the residue reaching the bottom surface (which is not warmed). Week by week, he perfects the layout to ensure adequate travel time for perfect drying. John has invented an arrangement to produce dehydrated (powdered) milk! Stored properly, powdered milk does actually last unimaginably long compared to the contemporary expectations.

The horse collar.

From Wikipedia:

A horse collar is a part of a horse harness that is used to distribute the load around a horse's neck and shoulders when pulling a wagon or plough. The collar often supports and pads a pair of curved metal or wooden pieces, called hames, to which the traces of the harness are attached. The collar allows the horse to use its full strength when pulling, essentially enabling the animal to push forward with its hindquarters into the collar. If wearing a yoke or a breastcollar, the horse had to pull with its less-powerful shoulders. The collar had another advantage over the yoke as it reduced pressure on the horse's windpipe.

From the time of the invention of the horse collar, horses became more valuable for plowing and pulling. When the horse was harnessed in the collar, the horse could apply 50% more power to a task in a given time period than could an ox, due to the horse's greater speed. Additionally, horses generally have greater endurance than oxen, and thus can work more hours each day. The importance and value of horses as a resource for improving agricultural production increased accordingly.

The horse collar was very important to the development of many areas of the world. Wherever oxen were used and could be replaced with horses, the use of horses boosted economies, and reduced reliance on subsistence farming. This allowed people more free time to take on specialized activities, and consequently to the development of early industry, education, and the arts in the rise of market-based towns.

The horse collar was developed in China in the 4th, possibly 5th century. It was not introduced into Europe until the 12th century.

To invent the horse collar in 5th century Europe, John will have to (1) remember roughly what it looked like, (2) realize what problems it solved, (3) obtain a horse, and (4) experiment. He should also interview anyone he can find who has been anywhere near China.

Saltpetre. Potassium nitrate. Explosives and firearms. Although he equally could have com from the past (and be South Asian) to 5th century Europe as the future. But gunpowder would only reach China in the 9th century, then Turkey, the Middle East, and finally Europe in the 13th century.

You asked, if it is "feasible" he could make this "invention" and "set up his 5th century worldwide business empire". This would allow him to establish a worldwide "empire" (no qualifications like "business" necessary), a good 800 years early.

And yes, with just a local blacksmith, etc. He just would have to know which rocks to use; and how not to make it NOT explode before he wanted it to, but um, that's the foundation for empire. Business comes afterward.

Guns&Cannons.

Now I know that a modern pistol or even older guns are no joke. They require a lot of work.

But many of the lessons that people learned the hard way can be skipped over as he already knows them.

Even an hour reading and seeing videos will provide enough information about the basic concepts of a gun.

He won't aim for an automatic rifle, not yet.

All he wants to make is a one shot gun of a sort or another.

He already saw a hundred revolver, he knows the trigger, the cartridge...etc. And smokeless self contained cartridges are not magic, they existed a long time ago.

So all he needs to do is experiment enough with gunpowder and machinery to create a gun. Even a single shot gun would be like magic at the time.

Starting with that he can make a fortune, and I mean a fortune, that will allow him to further improve his craft all the way to traditional revolvers.

He will have a monopoly and, if he invested sometime in it, can easily further improve metalworking and even machinery as a whole.

The YT channel forgotten weapons has amazing examples of people copying famous weapon designs with little tools and producing real guns.

Again all he want to make first is a single functional revolver.

All the other stuff, safety, standards, sights, rifling...etc come after he already make a lot of money.

Cannons are much "easier". Again just make one cannon and the local lord/jarl...etc would be so impressed that you will get enough money to make as many as you want.

Reading on those topics for a couple of hours would be enough to give theoretical knowledge.

I highly recommend he tries to do both in our world with limited tools to get a feeling of them though.

Aeolipile / Simple steam engine

The Aeolipile was made as a curiosity in the first century AD, its essentially a sphere filled with boiling water that has two exhaust pipes that allow the sphere to eject steam and spin the sphere.

I think an average person like John would know how to make a really simple steam engine like this and that using more water, more heat and bigger boiler could provide more power which makes it more useful.

Once you have a basic steam engine John knows enough history to figure out what comes next, lathe is an obvious first step, make an Aeolipile attach a rod on axis of rotation, skewer something on the rod and now you have a lathe. Power source for an Archimedes screw All of a sudden you now have a powerful siege weapon, a self running pump to drain your enemies water supply UP a hill as well as fast water distribution for permanent installs in cities. Grinders for metal work, windless windmills (just called "mills" if you will) for grain, etc...

All John needs to know is a steam engine is essentially a kettle with an exhaust pipe and that engines of any kind are really useful.

He will simply take seriously and push development what was seen as a mere novelty or curiosity.

since others bring invention from other region or just a view century later already, i may as well just jump to the wagon then.

heres mine

KITE

its easy to make and quite known for common folk and kid in this era, though i dont know is this true to modern western or specifically to john, you can use leather, cloth, or even use broad leaf as kite not necessary to be made from paper. it can help measure distance, testing wind, lifting men, and signal, or if you near shore you can help fishermen using kite fishing, also help proto benjamin franklin or even your john to proof regarding lightning and electricity theory thing and early air plane invention.

AIR BALOON

already known in china using sky lantern and even made from egg shell, can be use as alternative for kite stuff.

FORK OR OTHER FOOD UTENSILS

most europe people in that times eating using bare hands, this can help hygienic alot especially made of silver, this will be prestigious enough to captivate monarch at least. or john can try chopstick, it can be made from simple wood, precious metal/stone to ivory so it can also captivate monarch, and its quite simple enough and less material require, though need to teach them how to use it to make it a booming, which depend on do john know how to use chopstick or not, this can change european culture as a whole, or at least can make kebab booming earlier, since kebab exist since prehistoric, its meat in stick after all, but not that well used during this period.

PRINTING

like woodblock printing or xylograph and movable clay block press printing no machine required, it use by china and its simple enough, just add paint to the block and press it to the object, can be applied to even stone, and single man is enough to do single printing.

PAPER

ask the carpenter permissions to get the sawdust to get the fiber, asking farmer for their grass, put it into water and mix it, after cleaning it, boil it in water, beat or find something to flattened it until the fiber is thin, dry it, make paper, thats at least the crude way i know, the result is probably not as high grade paper today though, also i may make some mistake there but through trial and error it can be perfected.

• and if John come there with his modern clothing, it can also revolutionize clothing or fashion, such as sewing pattern/technique or clothing forms, heck even john way of wrapping clothes to look exotic without any sewing can boom a fashion and change european culture if it captivate the noble or merchant fashionista.

• also concrete or cement, it made of water, sand, and gravel. modern people may know this, even though they dont know the correct mixture same as me, though this depend on john knowledge.

• oh yeah also if John know how to make wax or clay, he can try make 3d map, akin to 3d printing stuff but more primitive (already a thing in ancient china btw, so basically most modern non electric invention is already an invention or figure out in other regions in the past, and most of it is far before 5th century even, including robot or automaton).

• since others says scientific theory is ok, maybe metric system or unified measurements (i dont know the correct english, i hope this is understandable enough regarding what i mean), since europe dont have base or unified measurement in that time or quite inconsistent as far as i know, i believe modern western know it well even without advance educations, though my math suck so i cant say much regarding it.

Basic maths using the Arabic (decimal) number system, basic economic theory and double entry book keeping.

This includes introducing the concept of zero. Basic statistics, compound interest formula's, forecasting, financial analysis and algebra and calculus. As a businessman he should hopefully be numerate and have and a high school education or better.

He would soon find himself in a senior administrative or teaching post. Better still his knowledge is portable and can't be stolen only learnt.

Amendment: Forgot to include concepts and formulas used in logistics, project management etc plus currency and commodities hedging**.

Another amendment; All the other inventions mentioned in this thread are worthy of development. The problem is the character by default knows about them but cannot (unless otherwise specified) re-invent them himself. So if he were just show up and to try and explain gunpowder or germ theory etc chances are he would be seen as either mad or a witch. BUT- after establishing himself as a mathematical prodigy and gaining peoples trust? Then he can start talking about how other scholars in his home land had studied these things and describe them in general. Result? before you know it experiments and new ideas start being conducted/tried across the land. And all because he's proved his worth first.

I'd honestly go for the printing press.

John doesn't really have to know how to make one, he just has to describe the basic pieces to a craftsman and demonstrate it to the right people.

It's utility would be obvious within a highly bureaucratic government structure.

It's utility would be obvious to the Church. Plenty of Catholic scholars in that century. Probably some Pagan ones, too.

The press doesn't require fancy knowledge or technology to make and can easily be operated by slaves, paid workers, or monks, depending. And eventually, people much more knowledgeable than John will work out the bugs and improve its design.

As far as world changing --- that's obvious! More books means higher likelihood of ancient works surviving to the present day. Will eventually mean a surge to the nascent scientific and scholarly explosion of the medieval period. Perhaps, in the hands of the right people, that revolution could be brought forward. We might be seeing proper universities 500 years before they got going in our timeline. We could see the invention of the scientific method much earlier.

Address to comments:

• what about paper? They have papyrus and they have vellum and they also have cloth. All of these can be printed on. They'll figure out rag paper soon enough! Or perhaps bark paper. Even regular leather can be printed on.
• Ink & metalwork? Do you think they didn't have ink and bronze and even iron in the 5th century AD? Anyway, all John needs to do is demonstrate how letters carved onto blocks of wood can be rearranged to print different words. His audience will take over from there!
• all John has to do here is plant the seed. This is why I specified him showing this to the Church: it is within the next three centuries that the Church will be rescuing the Empire from its own decay and bequeathing all the ancient knowledge on to the empires of the future
• trust me: if they lack rag paper in John's time, they will figure something out soon enough! Who knows? Maybe the libraries & universities of the 7th century will be founded on books of linen or amate!

Lenses

John does not knows how to precisely make lenses nor how to shape the glass into the correct form nor the mathematical optical formulas. However, he have some crude ideas of how they work. Also, he knows that it is (a) possible, (b) reachable with the 5th century technology and (c) revolutionary.

So, John just need to recruit some loyal people with good skills in glass-making and/or maths. In a few months, with some trial and error, he and his workers would be able to produce glasses for people with no good eyes, spyglasses for soldiers, and also telescopes and microscopes. And this would happen more than a thousand years before than when they were actually invented.

With a telescope, astronomers/astrologers would quickly start to use them to observe the skies and soon heliocentrism and gravitation would be figured out, much before than they actually did.

With microscopes, the microorganisms would be discovered and would help to make advances in medicine happen much faster. Also, it would also be used in other areas like metallurgy, alchemy and secure communications which would also enable further development in other areas.

In fact, lenses already existed in that age, but they were crude and not widely used. What he needs to do is to lead his workers to meticulously produce them in mass with the best quality achievable. And then, he just sells them, a skill that surely any good enterpreneur have.

"Lest darkness fall" protagonist made his first money in 6th century Europe by producing brandy. His revolutionary tool was "pot still" (though I don't know if it qualifies).

How about a compass? Even without detailed scientific knowledge it should be possible to make one with a bit of experimentation. Lode stones were known in ancient times as were various forms of iron. A bit of experimentation with small fragments / splinters from flattened nails and a lode stone should be able to produce a magnetised pointer. A small marked wooden box would be easy to make and even a small glass cover might be possible.

It would be of great use to mariners travelling across the Mediterranean.

Hygiene: A powerful battlefield weapon

If you really want to get the attention of powerful people, teach them how to keep their soldiers alive when the enemy is dying. Through much of history, diseases have ravaged armies around the world. Even with the improvements of technology made in the next 1,400 years, two-thirds of fatalities in the US Civil War came from disease. Start teaching a few things like not collecting drinking water downstream of your latrines. Then move on to advanced lessons, like hand washing and properly storing and cooking food. Charge heavily for each lesson. Then train employees to teach these skills and collect fees to have them go to every military unit in the country and explain hygiene.

Pros: You don't have to bring anything from the future and you can prevent a lot of human suffering.

Cons: You might upset the military balance of power with unknown consequences.

Eyeglasses. Glassmaking was millennia old by that point, some experimentation with lens shapes and a bit of uncomplicated metalwork later, and you've started improving vision. The aristocracy and the rich would pay through the nose for better sight as they get older.

Similarly, the telescope.

The printing press. The screw press was in use by the Romans by the 1st century, so no need to reinvent the wheel there, and the printing press is a relatively simple modification.

Even on the wikipedia list you provide, there are quite a few inventions that rely on principles so simple that even a layman would probably understand well enough to invent.

These include:

• The brace (and auger)
• The thermometer
• The coil spring (assuming ironworking is sufficiently advanced to make wire)
• Buttons (and buttonholes)
• Eyeglasses/Telescope/Microscope (it might take a layman a long time to get the specifics right, but I think they'd get it eventually)
• Barbed wire (assuming ironworking is sufficiently advanced to make wire)
• The zipper
• The hook-and-loop fastener (a.k.a. Velcro)
• Movable type and the printing press
• The hot air balloon (and thus flight!)
• Reinforced concrete
• The Windmill
• Banknotes (though it requires people to buy into the idea to be useful)
• Medical hygiene
• Variolation (The most rudamentary form of vaccine. You probably know the principle, though you probably don't know it by this name.)
• The pasteurization process

As well as the general idea for several other basic scientific principles. (E.g. the atomic nature of matter, and the parts of an atom).

Which one is the best? I would have to go with the hot air balloon. Inventing flight one and a half millennia early just seems so cool... and it would revolutionize exploration, travel, and warfare.

Since this question has the reality check tag, I'm going to have to point out that people in ancient times weren't stupid. They just lacked the means and the knowledge base. They were far more in tune with is possible with manual labour and handcrafting.

So for John, as uneducated as he is and with no research, to try and bring back a concept which they were not already aware of, yet have the means to achieve (both technically and economically) seems almost insurmountable to be. A lot of stuff we take for granted now, if it was doable back then was crazy expensive and so simply wasn't done.

If it's so basic that John is aware of it and they can do it, but they haven't done it, then they either don't need it or they need it but it is too expensive. Even if we put the technical hurdles specific to the product aside, the more challenging hurdle is to make it less expensive (aka feasible). That probably means enabling technologies which are the most challenging of all. You aren't inventing enabling technologies without knowing what you're doing, which John doesn't. The value of the enabling technology would also dwarf the value of any particular product.

You're on their turf, doing what they do, with their means, trying to outwit them with no preparation. I'm almost inclined to say it's modern hubris, which might just be up John's alley.

So I'm going to present this frame challenge: Are you wanting something that John would actually be believably successful commercializing? Or just something he thinks he would be successful at?

A laymen bringing back the concept of a steel hammer or lenses might as well be bring back the concept of a computer if he has no idea how to make steel or glass and forge them or grind them in the first place. Ideas are a dime a dozen.

John Is Not A Very Smart Man.

John needs to utilize something that already exists!

Penicillium, the mold that was discovered to contain a powerful antibiotic, would be an absolute historical game changer.

In Europe, the stirrup. They were in use in China by the fifth century, but were unknown in Europe, and give a very significant advantage to cavalry as well as facilitating other uses for ridden horses. The Wikipedia article says:

Some argue that the stirrup was one of the basic tools used to create and spread modern civilization, possibly as important as the wheel or printing press.