Differentiate 4x^2+4x+xy and 5 with respect to x and set them equal to each other. Remember that as you start to differentiate y with respect to x, y is actually y(x).
So (4x^2+4x+xy)' = 8x+4+y+xy' = (5)' = 0, and it follows that y' = (-y-8x-4)/x. We are given that (5, -23) is a point on the original function. So when x = 5, y'(5) = (-(-23) -8(5) -4)/5 = -21/5
[Note that when we differentiated xy, we used the product rule. That's where we got y + xy' above.]