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The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits firstand second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.