Answer: (y-5)(y+3)
// If the coefficient of the y^2 is 1 and equation has integer-solution, than 15 must be divisible to that solution. Fermat's Theorem consequence
It's obvious that y=5 is solution.
// If x1 and x2 are solution to quadratic equation, ay^2+bx+c, where a is 1, then x1*x2=c. Fermat's Theorem
Divide equation by (y-5), If you cannot do this look for other obvious solutions.