Let $L\left(G\right)$ denote the set of all odd cycle lengths of a graph $G$. Gyárfás gave an upper bound for $\chi \left(G\right)$ depending on the size of this set: if $\left|L\right(G\left)\right|=k\ge 1$, then $\chi \left(G\right)\le \mathrm{2k}+1$ unless some block of $G$ is a $K_{\mathrm{2k}+2}$, in which case $\chi \left(G\right)=\mathrm{2k}+2$. This bound is generally tight, but when investigating $L\left(G\right)$ of special forms, better results can be obtained. Wang completely analyzed the case $L\left(G\right)=\left\{3\text{,}5\right\}$; Camacho proved that if $L\left(G\right)=\{k\text{,}k+2\}$, $k\ge 5$, then $\chi \left(G\right)\le 4$. We show that $L\left(G\right)=\left\{5\text{,}7\right\}$ implies $\chi \left(G\right)=3$.