5.3 Find the range of the function $y=\sqrt{a+x}+\sqrt{b-x}\left(a, b \in \mathbf{R}^{+}\right)$.
5.3 In a circle with diameter $A B=\sqrt{a+b}$, take a point $C$ on one semicircle such that $A C=\sqrt{a+x}, B C=\sqrt{b-x}$, and take the midpoint $D$ on the other semicircle, $A D=B D=\sqrt{\frac{a+b}{2}} . \quad \sqrt{a+b} \leqslant y \leqslant \sqrt{2(a+b)}$.