The +/- J model is studied for the mixed spin-1/2 and 5/2 system on the Bethe lattice with the coordination numbers q = 3, 4 and 6 in terms of the exact recursion relations. The effects of varying the crystal field D and probability p are investigated on the phase diagrams of the model. The thermal variations of the order-parameters are also studied with the external magnetic field h is turned on and off. It is found that the model exhibits either second-or first-order phase transition lines on the (T, D) planes for given p values with 0 <= p <= 1. In addition, the phase diagrams on the (T, p) planes for given D show that two second-order phase transition lines combine with the tips of the same first-order phase transition line from above and below at two tricritical points. Our investigation has not revealed any compensation temperatures which may be caused by the large temperature differences between the magnetization curves belonging to spin-1/2 and 5/2. (C) 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.