A note on the maximum number of triangles in a C5-free graph

We prove that the maximum number of triangles in a C5-free graph on n vertices is at most 122(1+o(1))n3/2, improving an estimate of Alon and Shikhelman [Alon, N. and C. Shikhelman, Many T copies in H-free graphs. Journal of Combinatorial Theory, Series B 121 (2016) 146-172].