Prove that if $\displaystyle p \neq 5$ is an odd prime, prove that either $\displaystyle p^2-1$ or $\displaystyle p^2+1$ is divisible by 10.

My proof so far:

If $\displaystyle 10 | p^2-1$, then we are done. Assume 10 doesn't divide $\displaystyle p^2-1$.

Let p=2n+1 for some integer n. Then $\displaystyle p^2+1 = (2n+1)^2+1=4n^2+4n+1+1=4n^2+4n+2$ so 2 can divide it.