elementary number theory - Proof using exhaustion $n^4 - 1$ is divisible by $5$ where $n$ is not divisible by $5$.

The title pretty much states it.
Proof using exhaustion $n^4 - 1$ is divisible by $5$ where $n$ is not divisible by $5$.

Can anyone give me a hint how to approach this?

Do I need to consider separate case where n is odd and when n is even?

Solution: use division algorithm