How would you solve this A level style question?

This is the puzzle where I will be exploring some nice pieces of maths I talked about before. I am discussing this because in a recent class this problem came up and the entire class independently tried it and when we looked at our solutions, none of them were the same, but there were many different correct methods. Please write in the comments how you solved or tried to solve this problem. Here it is:

Prove that n⁵-n is divisible by 30, where n is a member of the natural numbers (ℕ)

I hope you enjoy!