Answer
$\frac{33}{65}$
Work Step by Step
1. Let $cos^{-1}\frac{5}{13}=u$, we have $cos(u)=\frac{5}{13}$ and $sin(u)=\frac{12}{13}$
2. Let $cos^{-1}\frac{4}{5}=v$, we have $cos(v)=\frac{4}{5}$ and $sin(v)=\frac{ 3}{5}$
3. Thus $sin(u-v)=sin(u)cos(v)-cos(u)sin(v)=(\frac{12}{13})(\frac{4}{5})-(\frac{5}{13})(\frac{3}{5})=\frac{33}{65}$
