Why does my 240V range outlet have five wires?

The wires you have here are ample for almost any range/oven configuration... almost.

Well, you definitely have conduit. The 3-wire entry above might've been /3 armored cable, but nobody makes armored cable with four #8? 10? red and one #14? 12? white. And if they did, they wouldn't mark "TW" on the wires. So the fat pipe is definitely conduit. Maybe so is the thin pipe.

I'm betting that metal conduit provides grounding. So you're all set for a modern 4-wire hookup.

Note that since it is conduit, it is feasible to pull out any wires you don't like, and replace them with wires you do like. This is a huge advantage over those poor people who have their oven wiring done in cable, and cannot replace that in-wall wiring without a bunch of carpentry, drywall and paint.

What do you have here now?

Your current wiring includes

• A 24 or 32 amp 120V/240V circuit for a range or oven (neutral for oven light),
• Another 24 or 32 amp 240V-only circuit that does not, and
• a 15 or 20 amp 120/240V circuit that can serve either a single oven (providing neutral for oven light) or a multi-wire branch circuit powering two 120V sub-circuits e.g. microwave + vent hood.

I can't tell if you have #8 or #10 wire on the big stuff, but regardless, let's crunch the numbers.

If you use both circuits in this pipe, then you need to contend with a thermal derate. Because of the nature of split-phase power, each circuit contains 2 wires "that count" under this table:

So... 24A for #10 and 32A for #8. This "TW" wire really ties your hands because it forces you to derate off the 60C column.

The TW wire is obsolete; it's been replaced with THW (H=High Temp: 75C) and finally THHN (90C). If you did nothing else, it'd be productive to pull these wires out of the conduit, drag in a pulling rope, then pull in the same wires that are THHN. That lets you run out of the 90C column, permitting 30A from #10* and 44A from #8 wire.

Or for that matter you could pull and replace exactly the wires you need now. To determine that, we need to see your oven's documentation. I do recommend using all-red for the hots, or a weirder color still, to signal to the next person that this is conduit and they can pull any wires they please.

* 32A by the math; but #10 can't exceed 30A because of NEC 240.4(D).