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.