5. In $\triangle A B C$, $A B=A C=7, B C=4$, point $M$ is on $A B$, and $B M=\frac{1}{3} A B$. Draw $E F \perp B C$, intersecting $B C$ at $E$ and the extension of $C A$ at $F$. Then the length of $E F$ is $\qquad$
5. $5 \sqrt{5}$