Embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property

Five 4-dimensional families of embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property (a_7j = b_j, 1 <= j <= 7, c_7 = 1) are derived. Previously known pairs satisfy simplifying assumption sum_j a_ij c_j = c_i^2 / 2, i >= 3, and constitute two of these families. Three families consist of non-FSAL pairs of 6-stage methods, as the 7th stage is not used.