Answer
\sin$tan(A-B) = \frac{63}{16}$
Work Step by Step
If the hypotenuse is 13, and the opposite side is 5, then the length of the adjacent side is $\sqrt{13^2-5^2} = 12$
If the hypotenuse is 5, and the adjacent side is 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$
$tan(A-B) = \frac{tan~A - tan~B}{1+tan~A~tan~B}$
$tan(A-B) = \frac{(\frac{5}{12}) - (-\frac{4}{3})}{1+(\frac{5}{12})(-\frac{4}{3})}$
$tan(A-B) = \frac{\frac{21}{12}}{\frac{9}{9}-\frac{5}{9}}$
$tan(A-B) = \frac{(\frac{7}{4})}{(\frac{4}{9})}$
$tan(A-B) = \frac{63}{16}$
