Pure quintic fields defined by trinomials

Pure quintic fields which can be defined by a trinomial X-5 + aX + b or X-5 + aX(2) + b, where a and b are nonzero rational numbers, are characterized. Using this characterization it is shown that the only pure quintic field Q(p(1/5)) (p a prime) which can be defined by a trinomial is Q(2(1/5)) = Q(theta), where theta is the unique real root of x(5) + 100x(2) + 1000 = 0.