Find the exact value of sin

Plug into the Sine subtraction formula which is sin(x - y) = sinxcosy - cosxsiny
So
First find the Cos of the values using a triangle and the Pythagorean theorem
Triangle X missing side =Sqrt(5^2 - 4^2) = 3
Triangle y missing side = sqrt(13^2 - 12^2) = 5
So we now plug it into the equation
(4/5)(5/13) - (3/5)(12/13)
Multiply
4/13 - 36/65 = -16/65