Or at least an intended one. It turns out that quintessential actually comes from quint, which of course means five. The Online Etymology Dictionary explains the source of quintessence:
early 15c., in ancient and medieval philosophy, "pure essence, substance of which the heavenly bodies are composed," literally "fifth essence," from Middle French quinte essence (14c.), from Medieval Latin quinta essentia, from Latin quinta, fem. of quintus "fifth"In other words (if I understand correctly) getting to the essence of something demanded going through five stages, the first four being the "known elements". Interestingly, in the case of Take Five it's not a distillation, a paring down, but actually an addition - of a beat.
A loan-translation of Greek pempte ousia, the "ether" added by Aristotle to the four known elements (water, earth, fire, air) and said to permeate all things. Its extraction was one of the chief goals of alchemy. Sense of "purest essence" (of a situation, character, etc.) is first recorded 1580s.