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g(x)=(2x−5)^3 and h(x)= square root cubed of x +5/2

are functions g(h(x)) and h(g(x)) inverses?

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The h(x) function IS THE INVERSE OF g PROVIDED WHAT YOU MEAN for h(x) is CUBE ROOT OF (x + 5/2).
 
Because in that case, g(f(x)) = x ... that's the criterion for mutual inverses.
 
Many students are not able to express, in words, a radical having 3 in its index (little number in the radical symbol's 'notch'.)    

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Paul M. | Learn "how to" do the math and why the "how to" works!Learn "how to" do the math and why the "...
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First, I suggest that you graph the two equations given.
2 functions which are inverses will be symmetric with respect to the line y = x.
 
Second to compute the inverse of g(x), write y = (2x-5)3 and then exchanges the roles of x and y, i.e.
x = (2y-5)3 and solve for y
 
x1/3 = 2y - 5 => x1/3 + 5 = 2y and y = (1/2)(x1/3 + 5)
 
Now add this function to your graph and look at the relation between this function and g(x)!