Providing the asymptotic lower and upper bounds of the following recurrence relation using a recursion tree with substitution method

$T(n) = T(\sqrt n) + 5$

I know that each $k$-th level is equal to $n^{1/2^k}$, and intuitively, $T(n) = \theta(\log_2(\log_2 n))$. I am just not certain where the constant 5 goes in the substitution method, and how I can generate tight lower and upper bounds for this recurrence relation.