5. If $x, y$ satisfy $|y| \leqslant 2-x$, and $x \geqslant-1$, then the minimum value of $2 x+y$ is
A. -7
B. -5
C. 1
D. 4
The graph of $|y|=2-x$ is symmetric about the $x$-axis, and the coordinates of the three vertices of the feasible region are $(-1,3),(-1,-3),(2,0)$. Therefore, the minimum value of $2 x+y$ is $2 \times(-1)-3=-5$, so the answer is $B$.