MathNet 2016-part-02 — 184 problems (EN–VI) Question 44

Let $p$ be a prime number greater than $5$. Suppose there is an integer $k$ satisfying that $k^2 + 5$ is divisible by $p$. Prove that there are positive integers $m$ and $n$ such that $p^2 = m^2 + 5n^2$.