The influence of increasing the coordination number q on the phase diagrams of the mixed spin-2 and spin-5/2 Blume-Capel Ising ferrimagnetic system with two crystal-field interactions, D-A for spin-2 and D-B for spin-5/2, is investigated on the Bethe lattice by using the exact recursion equations. The phase diagrams are obtained for the case with equal crystal field strengths when q = 3, 4 and 6 on the (kT/|J|, D/|J|) planes and for the case with unequal crystal field strengths on the (kT/|J|, D-A/|J|) and (kT/|J|, D-B/|J|) planes for various values of D-B/|J| and D-A/|J|, respectively, for q = 4 and 6. Besides the second-order lines, the model presents three types of first-order phase transition lines; one of them ends on the compensation lines (q = 3), the other one ends at a critical end point (q = 4) and last one terminates at a tricritical point (q = 6) for the case with equal crystal field strengths. In this case we have also observed up to four compensation temperatures when q = 6. Besides the second-order, tricritical and compensation lines, the system presents two types of the first-order lines one of them ending at a tricritical point and the other one ending at an isolated point when unequal crystal field values are taken. (C) 2007 Elsevier B.V. All rights reserved.