5. Given $x, y \in \mathbf{R}_{+}$. Then the maximum value of $\frac{x}{2 x+y}+\frac{y}{x+2 y}$ is ( ).


5. B.

Let $s=2x+y, t=x+2y$. Then
$$
\begin{array}{l}
x=\frac{1}{3}(2s-t), \\
y=\frac{1}{3}(2t-s) .
\end{array}
$$
$$
\text{Thus } \frac{x}{2x+y}+\frac{y}{x+2y}=\frac{4}{3}-\frac{1}{3}\left(\frac{t}{s}+\frac{s}{t}\right) \leqslant \frac{2}{3} \text{. }
$$