We generalize recent results regarding the phase space of the mass deformed E-1 fixed point to a full class of five-dimensional superconformal field theories, known as X-1,X-N. As in the E-1 case, a phase transition occurs as a supersymmetry preserving and a supersymmetry breaking mass deformations are appropriately tuned. The order of such phase transition could not be unequivocally determined in the E-1 case. For X-1,X-N, instead, we can show that at large N there exists a regime where the phase transition is second order. Our findings give supporting evidence for the existence of non-supersymmetric fixed points in five dimensions.
