To solve this equation, we will first distribute each set of parentheses and combine like terms:

(x+4)(x+5) = x^2 + 5x + 4x + 20 = x^2 + 9x + 20

-7(x+8) = -7x - 56

So, the original equation becomes:

(x^2 + 9x + 20) - x + 5x - 7x - 56 = 13

Next, combine like terms:

x^2 + 7x - 36 = 13

Now, subtract 13 from both sides:

x^2 + 7x - 36 - 13 = 0

x^2 + 7x - 49 = 0

Now, we can factor the quadratic equation:

(x + 7)(x - 7) = 0

Setting each factor to zero gives us the solutions:

x + 7 = 0 or x - 7 = 0
x = -7 or x = 7

Therefore, the solutions to the equation (x+4)(x+5)-x"+5x-7(x+8)=13 are x = -7 and x = 7.