To solve this equation, we need to simplify the right side first by combining like terms:

(3x + 3 - x^2 + 5) simplifies to (-x^2 + 3x + 8)

So the equation becomes:

10/(x-5)(x+1) = (-x^2 + 3x + 8)/(x-5)(x+1)

Now we can cross multiply to solve for x:

10(x-5)(x+1) = (-x^2 + 3x + 8)

Expanding both sides:

10(x^2 - 4x - 5) = -x^2 + 3x + 8

10x^2 - 40x - 50 = -x^2 + 3x + 8

Rearranging the terms:

11x^2 - 43x - 58 = 0

Now we have a quadratic equation that we can solve using the quadratic formula:

x = [-(-43) ± sqrt((-43)^2 - 4(11)(-58))] / 2(11)

x = [43 ± sqrt(1849 + 2536)] / 22

x = [43 ± sqrt(4385)] / 22

x = [43 ± 66.19] / 22

x = 109.19 / 22 or -23.19 / 22

x = 4.96 or -1.05

Therefore, the solutions to the equation are x = 4.96 and x = -1.05.