5. Let the base of the right quadrilateral prism $A^{\prime} B^{\prime} C^{\prime} D^{\prime}-A B C D$ be a rhombus, with an area of $2 \sqrt{3} \mathrm{~cm}^{2}, \angle A B C=60^{\circ}, E$ and $F$ be points on the edges $C C^{\prime}$ and $B B^{\prime}$, respectively, such that $E C=B C=$ $2 F B$. Then the volume of the quadrilateral pyramid $A-B C E F$ is ( ).
(A) $\sqrt{3} \mathrm{~cm}^{3}$
(B) $\sqrt{5} \mathrm{~cm}^{3}$
(C) $6 \mathrm{~cm}^{3}$
(D) $\dot{9} \mathrm{~cm}^{3}$
5.A.

On the base $ABCD$, take the midpoint $K$ of $BC$, and connect $AK$. From the given information and the properties of a right prism, we get $AK \perp$ plane $BCEF$. Therefore, $AK$ is the height of the pyramid $A-BCFE$.
$$
\begin{array}{l}
BC=AB=AC=2, AK=\sqrt{3}, CE=2, BF=1 . \\
\text { Thus, } V_{A-BCFE}=\frac{1}{3} S_{\text {trapezoid } EFB C} \cdot AK=\sqrt{3}\left(\mathrm{~cm}^{3}\right) .
\end{array}
$$