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
5. B.

The given conditions are equivalent to
$$
\left\{\begin{array}{l}
-1 \leqslant x \leqslant 2 \\
y \leqslant 2-x \\
x-2 \leqslant y .
\end{array}\right.
$$

By plotting the feasible region, we know that $2x + y$ achieves its minimum value of -5 when $x = -1$ and $y = -3$.