I have this very basic number theory type proof that is causing me some headaches and I know it is probably very simple.
I want to prove that if $5|n^3$ then $5|n$.
I have a condition that I am imposing here, one cannot use GCD function.
It is quite obvious to me that $5|n$, due to the fact that $n^3$ is $n*n*n$, and when dividing by $5$, its obvious that it must divide into one of the duplicate '$n$' here. I am not sure if this can be done via a contrapositive proof or proof by contradiction. It seems to me that it can be done via a direct proof.
So if someone can help with a proof of this, would really appreciate it.