The magnetic properties of a ferrimagnetic mixed spin‐3/2 and spin‐5/2 Ising model with two crystal fields, in a longitudinal magnetic field, are studied by Monte Carlo simulations. The role of the different interactions in the Hamiltonian is explored. We investigate the thermal variations of the total magnetization and present phase diagrams. Depending on the region of the parameter space, we find some interesting phenomena such as compensation temperatures, and discontinuities in the magnetizations. We find that when an external field is present, the discontinuities are due to a simultaneous reversal of the spins of the sublattices. They signal the change between two different antiferromagnetic orderings, and are basically due to a competition between the different interactions in the Hamiltonian. We plot the dependence of the temperature at which the new phase occurs, for the different parameters in the Hamiltonian. Our results differ radically from earlier results obtained by other authors based on mean field theories. We find compensation temperatures at some particular combinations of parameters. Mean field theory predicts a wide range of parameters where the system presents even several compensation temperatures; in most of these regions we found none. In contrast with the mean field analysis that only looks at the total magnetizations, our study includes an analysis of the behavior of the sublattice magnetizations.