Proof Writing & Problem Solving · Easy problem

To prove "if $5 \mid n^2$ then $5 \mid n$", prove the contrapositive: if $5 \nmid n$, then $n^2$ leaves a nonzero remainder on division by $5$. Checking $n = 5k + 1, 5k + 2, 5k + 3, 5k + 4$, what is the sum of the different remainders that $n^2$ can leave?