The effects of assuming equal or unequal crystal fields (CF) on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice (BL). The equal CF case was considered for the coordination numbers q = 3, 4, and 6, while for q = 3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q = 4 and first-order phase transitions and tricritical point (TCP) for q = 6. In the unequal CF case for q = 3, the system yields first-and second-order phase transitions, TCP's, and three compensation temperatures. In addition, the TCP's in a very short range are classified as the stable and unstable ones depending on their free energies.