Presumably you do know that and . Since you know sin(B) and cos(A) (and know that the angles are acute) you can solve for cos(B) and sin(A).
Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator
cos (A + B)
Here is my take on the question.
cos (A + B)
= cosAcosB - sinAsinB
= (4/5)cosB - sinA(5/13)
After this, I don't know how to continue. Answer is 33/65