5. Point $P(x, y)$ satisfies the planar region
$$
\left\{\begin{array}{l}
\cos \theta \leqslant x \leqslant 3 \cos \theta, \\
\sin \theta \leqslant y \leqslant 3 \sin \theta
\end{array}(\theta \in \mathbf{R}),\right.
$$

Point $M(x, y)$ satisfies
$$
(x+5)^{2}+(y+5)^{2}=1 \text {. }
$$

Then the minimum value of $|\overrightarrow{P M}|$ is ( ).
(A) $2 \sqrt{2}-1$
(B) $4 \sqrt{2}-1$
(C) $6 \sqrt{2}-1$
(D) $\sqrt{61}-1$
5. D.

Notice that, point $P$ satisfies the planar region which is part of an annulus centered at the origin:
$$
1 \leqslant x^{2}+y^{2} \leqslant 9(x \geqslant 0, y \geqslant 0) .
$$

Therefore, the minimum value of $|\overrightarrow{P M}|$ is
$$
\sqrt{(1+5)^{2}+(0+5)^{2}}-1=\sqrt{61}-1 \text {. }
$$