5. Quadrilateral $A B C D$ is a rhombus with side length $a$, $\angle B A D=60^{\circ}$, when folded along the diagonal $B D$ to form a dihedral angle $A-B D-C$ of $120^{\circ}$, the distance between $A C$ and $B D$ is $\qquad$ .
$\frac{\sqrt{3}}{4} a$