HMMT November 2016 T6

Let $A B C$ be a triangle with $A B=5, B C=6$, and $A C=7$. Let its orthocenter be $H$ and the feet of the altitudes from $A, B, C$ to the opposite sides be $D, E, F$ respectively. Let the line $D F$ intersect the circumcircle of $A H F$ again at $X$. Find the length of $E X$.