To find the composition functions, we substitute the given functions into each other according to the provided equations.

H(f(x)):
H(f(x)) = H(-2x"+3x-5)
H(f(x)) = 2(-2x"+3x-5) - (-2x"+3x-5)"-3
H(f(x)) = -4x"+6x-10 + 3x-5-3
H(f(x)) = -4x"+9x-18

f(4(x)):
f(4(x)) = -2(4x+2)"+3(4x+2)-5
f(4(x)) = -2(4x+2)" + 12x+6 - 5
f(4(x)) = -32x" - 12x - 4 + 12x+6 - 5
f(4(x)) = -32x" - 1

Therefore, the compositions are: