how many solution(s) x^3= 125

There is only one solution for the equation x^3 = 125, which is x = 5.

what about x^2 = -16

For the equation x^2 = -16, there are two solutions. Since the square of any real number is non-negative, there are no real solutions to this equation. However, in the complex number system, the two solutions are x = 4i and x = -4i.