5. The eight vertices of the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$ are all on the surface of sphere $O$, where,
$$
A A_{1}=1, A B=2 \sqrt{2}, A D=3 \sqrt{3} .
$$

Then the spherical distance between points $B$ and $C$ is ( ).
(A) $\frac{2 \pi}{3}$
(B) $\frac{4 \pi}{3}$
(C) $2 \pi$
(D) $4 \pi$
5. C.

The radius of sphere $O$ is
$$
R=\frac{1}{2} \sqrt{1+(2 \sqrt{2})^{2}+(3 \sqrt{3})^{2}}=3 \text {. }
$$

In $\triangle O B C$,
$$
O B=O C=3, B C=A D=3 \sqrt{3} \text {, }
$$

then $\cos \angle B O C=-\frac{1}{2}$.
Thus, $\angle B O C=\frac{2 \pi}{3}$.
Therefore, the spherical distance between points $B$ and $C$ is
$$
2 \pi \times 3 \times \frac{1}{3}=2 \pi \text {. }
$$