First, we will distribute the terms:

(5-x)(x+5) = 5x + 25 - x^2 - 5x

x(x+10) = x^2 + 10x

Now, we will add these two expressions together and set them equal to 0:

5x + 25 - x^2 - 5x + x^2 + 10x = 0

5x + 25 - 5x + 10x = 0

25 + 10x = 0

10x = -25

x = -2.5

Therefore, the solution to the equation (5-x)(x+5)+x(x+10) = 0 is x = -2.5.