If x=k is a zero of a polynomial, then (x-k) is a factor in the polynomial.
So with roots at x = -2 , x = 3, and x = 5, you have
(x+2)·(x-3)·(x-5)
Now the "double root" means that you have that factor twice
(x+2)·(x-3)·(x-5)·(x-5)
but we'd normally write that with an exponent:
(x+2)·(x-3)·(x-5)^2
So y = (x+2)·(x-3)·(x-5)^2 is your equation.