PMO 2018 Problem 1

In triangle $ABC$ with $\angle ABC = 60^{\circ}$ and $5AB = 4BC$ , points $D$ and $E$ are the feet of the altitudes from $B$ and $C$ , respectively. $M$ is the midpoint of $BD$ and the circumcircle of triangle $BMC$ meets line $AC$ again at $N$ . Lines $BN$ and $CM$ meet at $P$ . Prove that $\angle EDP = 90^{\circ}$ .