Answer
$\frac{33}{65}$
Work Step by Step
Step 1. Letting $tan^{-1}(\frac{5}{12})=u$, we have $tan(u)=\frac{5}{12}$, thus $sin(u)=\frac{5}{13}, cos(u)=\frac{12}{13}$
Step 2. Letting $sin^{-1}(-\frac{3}{5})=v$, we have $sin(v)=-\frac{3}{5}$, thus $cos(v)=\frac{4}{5}$
Step 3. $cos(u-v)=cos(u)cos(v)+sin(u)sin(v)=(\frac{12}{13})(\frac{4}{5})+(\frac{5}{13})(-\frac{3}{5})=\frac{48-15}{65}=\frac{33}{65}$
