We have employed the Oguchi approximation (OA) to investigate the effects of a random crystal field which is active (inactive) with probability p (1-p) for given lattice sites on the thermodynamic properties of the mixed spin-(5/2,1/2) anisotropic Heisenberg model in the presence of an external magnetic field. By exploiting the thermal variations of the order parameters, interesting phase diagrams are produced on various planes. The phase diagrams show first- and second-order transition lines and also tricritical points. In addition to the reentrant behavior which is localized in a certain range of p at very low temperature, the magnetic exponent beta calculated near the critical point exhibits interesting behaviors depending on the crystal field interaction. The hysteresis behavior of the model is also investigated and it reveals that the width of hysteresis loop decreases or increases, respectively, for negative or positive crystal field region as the probability p increases.