It must be of minimum degree 3. Assuming a leading coefficient of 1, and knowing that the complex conjugate of a complex zero is also a zero (in order to have real coefficients),
p(x) = [x - (-3)] [x - (-5i)] (x - 5i)
p(x) = (x + 3)(x + 5i)(x - 5i)
(x + 5i)(x - 5i) = x2 - (5i)2 = x2 + 25
p(x) = (x + 3)(x2 + 25)
You should have no trouble finishing from here.