smc

Since the triangles are similar, we know that the corresponding sides of the triangle are in ratio to each other. We have $\frac{\overline{AB}}{\overline{XY}}=\frac{\overline{BC}}{\overline{YZ}}$. Plugging in values we have: $\frac{3}{4}=\frac{5}{\overline{YZ}}$. Solving for $\overline{YZ}$, we have $\overline{YZ}=6\frac{2}{3}$. So, the answer is $\boxed{6\frac{2}{3}}$.