A calculus problem by krishna havish

Let $x,y,z$ be positive numbers whose sum is $\frac \pi2$ .

If $A = \tan x \cdot \tan y + 5$ , $B = \tan y \cdot \tan z + 5$ , $C = \tan z \cdot \tan x + 5$ .

Find the maximum value of $A^{1/2} + B^{1/2} + C^{1/2}$ .