Geometry: Power of a Point & Mass Points · Medium problem

In $\triangle ABC$, $AB = 8$, $BC = 7$, and $CA = 5$. A circle passes through $B$ and $C$, meeting side $AB$ again at $E$ and side $AC$ again at $F$. Given that $AE = 3$, find the length $EF$.

Express your answer as a common fraction.