Define
F(n) = T(2^n)
Then we have that
F(n) = 4F(n/2) + 5
By the master theorem, we have that
a = 4
b = 2
f(n) = 5 = O(1) = O(m^0), so c = 0
0 < 2 = log_2(4)
So we're in case 1 of the master theorem. By case 1, we have
F(n) = Theta(n^2)
So
T(2^n) = Theta(n^2)
Therefore
T(n) = Theta(log(n^2)) = Theta(2logn) = Theta(log n)
So yes, your answer seems to be correct.