Question 159
Let $ABC$ be a triangle with $AB=5$, $BC=6$, and $AC=7$. 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 $DF$ intersect the circumcircle of $AHF$ again at $X$. Find the length of $EX$.