What is the range of the function y= ^3 square root x-5

This is the concept of algebra:
y=^3sqrt(x-5) can be written as:

y=(x-5)^(1/3)

Given that y=0 at the point x=5, that is:

when x=5 then

y=(5-5)^(1/3)

y=0^(1/3)

y=0

from the above we conclude that the domain is:

{x∈ R: x≥5}
That means that the domain is all real numbers greater than or equal to 5.