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