Answer
$-\frac{56}{65}$
Work Step by Step
$\cos A$ is positive as $A$ is in the fourth quadrant.
$\cos A=\sqrt {1-\sin^{2}A}=\sqrt {1-(-\frac{3}{5})^{2}}=\frac{4}{5}$
$\cos B$ is negative as $B$ is in the second quadrant.
$\cos B=-\sqrt {1-\sin^{2}B}=-\sqrt {1-(\frac{12}{13})^{2}}=-\frac{5}{13}$
$\cos(A-B)=\cos A\cos B+\sin A\sin B$
$=(\frac{4}{5})(-\frac{5}{13})+(-\frac{3}{5})(\frac{12}{13})=-\frac{56}{65}$
