If g(x) = x3 - 5 and h(x) = 2x - 2, then h(g(-2))= ?

Please, write "x^3" for "the cube of x," not "x3."  "^" denotes exponentiation.

Then you have g(x) = x^3 - 5 and (I assume) h(x) = 2x - 2.

1)  evaluate g(x) at x = -2:  g(-2) = (-2)^3 - 5 = -8 - 5 = -13

2) let the input to h(x) be -13:  h(-13) = 2(-13) - 2 = -28 (answer)