For all $nge 9$, we show that the only triangle-free graphs on $n$ vertices maximizing the number $5$-cycles are balanced blow-ups of a 5-cycle. This completely resolves a conjecture by ErdH{o}s, and extends results by Grzesik and Hatami, Hladky, Kr{a}l, Norin and Razborov, where they independently showed this same result for large $n$ and for all $n$ divisible by $5$.
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