(y-5)^48 = 96^32
(y-5) = 96^(32/48)
(y-5) = 96^(2/3)
(y-5) = (4^2)^(2/3)
(y-5) = 4^(2*2/3)
(y-5) = 4^(4/3)
(y-5) = 4^1.33

Now, we need to solve for y:

(y-5) = 5.278
y = 10.278

Therefore, the solution to the equation (y-5)^48 = 96^32 is y = 10.278.