5. Given that the projection of an equilateral triangle $ABC$ on plane $\alpha$ is a triangle with side lengths of $2, 3, 2\sqrt{3}$, then the side length of the equilateral triangle $ABC$ is
A. $2\sqrt{3}$
B. $\sqrt{13}$
C. $\sqrt{15}$
D. 4
Given $A A_{1}=x, C C_{1}=y$, then we have
$$
12+x^{2}=4+y^{2}=9+(y-x)^{2} \Rightarrow x=1, y=3 \text {. }
$$

Thus, the side length of the equilateral triangle $A B C$ is $\sqrt{13}$, so the answer is $B$.