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In this paper, we prove that any simple $\{C_3,C_5\}$-free non-emptyconnected graph $G$ with LLY curvature bounded below by $\kappa>0$ has theorder at most $2^{\frac{2}{\kappa}}$. This upper bound is achieved if and onlyif $G$ is a hypercube $Q_d$ and $\kappa=\frac{2}{d}$ for some integer $d\geq1$.

A tight bound on $\{C_3,C_5\}$-free connected graphs with positive Lin-Lu-Yau Ricci curvature