5. The number of integer solutions $(x, y)$ for the equation $\sqrt{x}+\sqrt{y}=\sqrt{336}$ is ( ).
(A) 2
(B) 3
(C) 4
(D) 5
5. D $x, y$ are both positive integers, and $\sqrt{x}, \sqrt{y}$, when simplified, should be like radicals with $\sqrt{336}$ simplified to $4 \sqrt{21}$.

Let $\sqrt{x}=m \sqrt{21}, \sqrt{y}=n \sqrt{21}$. Then $m+n$ $=4$ (where $m, n \geqslant 0$ and are positive integers). The values are
$$
(0,4),(1,3),(2,2),(3,1),(4,0) \text {. }
$$

The corresponding $(x, y)$ are
$$
(0,336),(21,189),(84,84),(189,21),(336,0) \text {. }
$$