A rectangle $ABCD$ stands with side $AB$ on the ground and with side $BC$ against the wall. The length of the side $AD$ is $4$, the length of the side $CD$ is $3$, and the length of the diagonal $AC$ is $5$. The rectangle is tilted with point $A$ as the pivot point such that point $C$ is straight above point $A$.

In this situation, what is the distance from point $B$ to the wall?
A) $\frac{2}{3}$
B) $\frac{3}{5}$
C) $\frac{5}{8}$
D) $\frac{7}{12}$
E) $\frac{8}{13}$