Erdős's conjecture on 5-cycles in triangle-free graphs

Let $G$ be a triangle-free graph on $n$ vertices. Erdős's conjecture. The graph $G$ contains at most $(n/5)^5$ cycles of length $5$. The balanced blow-up of the $5$-cycle $C_5$ attains this bound when $n$ is divisible by $5$, but the source gives no resolution of the conjecture.