Precalculus, Chapter 5, 5.4, Section 5.4, Problem 42

Given sin(u)=5/13,cos(v)=-3/5
Angles u and v are in quadrant 2.
A right triangle can be drawn in quadrant 2. Since sin(u)=5/13 you know that the side opposite of angle u is 5 and the hypotenuse is 13. Using the pythagorean theorem the third side of the triangle is 12.
A right triangle can be drawn in quadrant 2 since cos(v)=-3/5 you know
that the side adjacent to angle v is 3 and the hypotenuse is 5. Using the pythagorean theorem the third side of the triangle is 4.
cos(u-v)=cos(u)cos(v)+sin(u)sin(v)
cos(u-v)=(-12/13)(-3/5)+(5/13)(4/5)=36/65+20/65=56/65