Answer
$\frac{33}{65}$
Work Step by Step
Step 1. Letting $cos^{-1}\frac{5}{13}=x$, we have $cos(x)=\frac{5}{13}$ and $sin(x)=\frac{12}{13}$
Step 2. Letting $cos^{-1}\frac{4}{5}=y$, we have $cos(y)=\frac{4}{5}$ and $sin(y)=\frac{3}{5}$
Step 3. We have $sin(x-y)=sin(x)cos(y)-cos(x)sin(y)=(\frac{12}{13})(\frac{4}{5})-(\frac{5}{13})(\frac{3}{5})=\frac{33}{65}$
