JBMO 2011 Problem 2

Find all primes $p$ such that there exist positive integers $x,y$ that satisfy $x(y^2-p)+y(x^2-p)=5p$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.