To solve this equation, we first expand and simplify each term:

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

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

= 5x + x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 + 4 - x^3

Now combine like terms:

= x^3 + 5x + 2x^2 + 4x - 2x^2 - 4x - x^3 + 4 - 8

= x^3 - x^3 + 2x^2 - 2x^2 + 5x + 4x - 4x - 4 - 8

= 5x - 12

Now we have:

5x - 12 = 10

Add 12 to both sides:

5x = 22

Divide by 5:

x = 22/5 or 4.4

Therefore, the solution to the equation is x = 4.4.