Answer
$sin(A+B) = \frac{33}{65}$
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 $\sqrt{5^2-3^2} = 4$
$sin(A+B) = sin~A~cos~B+sin~B~cos~A$
$sin(A+B) = (\frac{5}{13})(-\frac{3}{5})+(\frac{12}{13})(\frac{4}{5})$
$sin(A+B) = -\frac{15}{65}+\frac{48}{65}$
$sin(A+B) = \frac{33}{65}$
