late 15c., quinqueniale, "lasting five years," from Latin quinquennalis "occurring once in five years, celebrated every fifth year," from quinquennis "of five years," from from quinque "five" (from PIE root *penkwe- "five"). With the ending perhaps influenced by Latin biennium etc.
Meaning "happening once every five years" is attested from c. 1600. In the inclusive reckoning that prevailed in the ancient world, the equivalent words meant "recurring every five years," reckoning both years of occurrence (by our uses, it would be "recurring every four years"), so that the Olympian games were, to the ancients, quinquennials.
As a noun, "a period of five years," from 1895; earlier quinquennal (1610s), quinquennium (1620s), and later quinquenniad (1842). The quinquennalia were Roman public games celebrated every fifth year.