To solve this equation, we can cross multiply to get:

(7x + 5)(x + 8) = (5x + 7)(x + 8)

Expanding both sides:
7x^2 + 56x + 5x + 40 = 5x^2 + 7x + 40
7x^2 + 61x + 40 = 5x^2 + 7x + 40

Subtracting 5x^2 + 7x + 40 from both sides:
2x^2 + 54x = 0

Factoring out a 2x:
2x(x + 27) = 0

Setting each factor to 0:
2x = 0 and x + 27 = 0

Solving for x:
2x = 0
x = 0

x + 27 = 0
x = -27

Therefore, the solutions to the equation are x = 0 and x = -27.