A Latin word that is like the word "trinity" but for "five fold" or "five as one"

What about penta- from Greek and used in Latin:

a combining form occurring in loanwords from Greek, meaning “five” ( Pentateuch); on this model, used in the formation of compound words ( pentavalent).

A trinity can still just mean three of something — the Christian doctrine of the Trinity is an assigned meaning rather than one inherent in the word. The three-in-oneness of the Godhead is expressed in triune. Sometimes Latin derivatives don't want to count past three: primary, secondary, tertiary; or even purely English once, twice, thrice, but a five-member brass ensemble is a quintet, and five infants born at the same time to one mother — a different form of the five-in-one you seek — are quintuplets.

This would suggest quintity, as it did to the members of the German brass quintet Quintity. Though the word hasn't made it into any dictionary to designate five of something, it would still be understood. Quintune, however, would be another story, but get enough people to use the word in the sense you assign and there you go. That's the way language works.

The corresponding analog to binary is quinary without a t, so if you prefer quinity and quinune, that would work as well.

Quincunx is not exactly what you asked for, but it can be pretty close when used in a very slightly metaphorical sense:

an arrangement of five objects, as trees, in a square or rectangle, one at each corner and one in the middle.

It all depends on how you would use it exactly. In the slightly metaphorical/loose sense, you could say something like this:

In the middle of the floor, a quincunx of formidable ladies were overseeing arrangements.

It would not be too far an extension to speak of a quincunx of major deities in a certain religion.

A somewhat less poetic term is quintet, which can be basically an group of five elements/people.

Edit: I see Rob's excellent comment above now. I would say pentad is also an excellent choice, which is like triad and has a meaning very similar to trinity.

Quintology is a nice word, but it only applies to logoi, i.e. words, theories, literature and the like.

Tchrist's cinquain is aequally nice. I suppose it would be a metaphor, though, because it is normally restricted to a group of five verses (lines in a poem).

P.S. I really think three is much better. Who would find five heads convenient?