To solve the equation 5sin(π/3 + x) + 7(π/3 - x) = 0, we need to use trigonometric identities to simplify it.

First, we expand the expression:

5sin(π/3 + x) + 7(π/3 - x) = 0
5sin(π/3)cos(x) + 5cos(π/3)sin(x) + 7(π/3) - 7x = 0
5(√3/2)cos(x) + 5(1/2)sin(x) + 7(π/3) - 7x = 0
(5√3/2)cos(x) + (5/2)sin(x) + 7(π/3) - 7x = 0

Now, we can rewrite the equation as:

(5√3/2)cos(x) + (5/2)sin(x) + 7(π/3) = 7x

Next, we can use the identity sin(α)cos(β) + cos(α)sin(β) = sin(α+β) to simplify:

sin(π/3 + x) = sin(π/3)cos(x) + cos(π/3)sin(x) = (√3/2)cos(x) + (1/2)sin(x)

Therefore, the equation becomes:

5sin(π/3 + x) + 7(π/3 - x) = 0
5(√3/2)cos(x) + 5(1/2)sin(x) + 7(π/3) - 7x = 0
5sin(π/3 + x) + 7(π/3 - x) = 0
5(√3/2)cos(x) + 5(1/2)sin(x) + 7(π/3) - 7x = 0
(5√3/2)cos(x) + (5/2)sin(x) + 7(π/3) - 7x = 0

This equation does not simplify further without knowing the specific values of x. To solve for x, you would need to use numerical methods or other techniques.