I have a question:

Prove that $\displaystyle n^{5}-n $ is divisible by 10 for all $\displaystyle n\ge2 $.

Since my current chapter is on induction, I figure it has something to do with induction, I don't really know. But all the induction I've learned in this chapter looks something like

$\displaystyle 2,6,12...n(n+1) = \frac{n(n+1)(n+2)}{3}$ etc..

Any help?