The Erdős Pentagon problem asks to find an n-vertex triangle-free graph that is maximizing the number of 5-cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladký, Král', Norin, and Razborov. Recently, Palmer suggested the general problem of maximizing the number of 5-cycles in K k+1free graphs. Using flag algebras, we show that every K k+1 -free graph of order n contains at most 1 10k 4 (k 4 − 5k 3 + 10k 2 − 10k + 4)n 5 + o(n 5 ) copies of C 5 for any k ≥ 3, with the Turán graph begin the extremal graph for large enough n.