The first thing that comes up is the five constant virtues (五常 or 五倫, which latter just happens to have the same sound as 五輪 here in Korean): https://en.wikipedia.org/wiki/Three_Fundamental_Bonds_and_Five_Constant_Virtues which are benevolence (인 仁), righteousness (의 義), propriety (예 禮), wisdom (지 智), and trustworthiness (신 信), or as Confucius has it:
父子有親(부자유친): a father's closeness to his child
君臣有義(군신유의): a lord's righteousness to his retainer
夫婦有別(부부유별): a husband's independence from his wife
長幼有序(장유유서): the elderly's putting in order of the youth
朋友有信(붕우유신): trust between friends
There's also The Book of the Five Rings by MIYAMOTO Musashi: 오륜서 where this exact term 五輪 represent the five Buddhist elements: earth, water, fire, air, and void. It's not commonly used, though, and only for what they symbolically represent. What we think of rings in the Olympic rings, the actual shapes, are called (5개의) 원 or (5개의 얽힌) 고리 as they're (five linked) loops, and rings for your fingers are (5개의) 반지.
Oh, and I forgot to mention, it's 오륜 only as a name, otherwise they'll write it 5륜 (5輪) which gets things with five wheels (or five flowers). Sorry for the length . . .