Originally Posted by
Анатолий год - годы
лето - лета
человек - люди
ребёнок - дети
1 ребёнок, двое детей, трое детей, ...
1 человек, 2 человека, 3 человека...
The origin of 5 -... лет is from лето -лета (summer - summers)
лета - summers sounded more poetic than годы - years but that's historically, it's now incorrect to say 5 годов, you must say 5 лет.
Also note that
21, 31 ... рубль, год is always- Nominative Singular,
22 - 24, 32- 34, ... рубля, года - Genitive Singular
5 - 20, 25 - 30 , 35 - 40, 45 - 55 ...рублей, лет - Genitive Plural
It gets more coplicated when those expressions are used in sentences, e. g. "Не хватает пяти рублей", "Она вырастила пятерых детей", etc.
Сколько лет, сколько зим! - How many summers, how many winters! (= Long time - no see!)
As saibot said above, it's something you have to memorise, like we have to with child - children, woman - women, etc.