The exchange anisotropy and crystal field effects for the mixed spin-2 and spin-1/2 Heisenberg model are studied on a square lattice by using the Oguchi approximation. Thermal behaviors of the order-parameters, i.e., magnetizations and quadrupole moment, and free energy are investigated to obtain the possible phase diagrams of the model. Not only the stable solutions but also the possible unstable solutions of the model are illustrated on the phase diagrams. Ten topological phase diagrams are presented which is just enough to understand the critical behavior of the model. It is found that the model yields both second- and first-order transitions, in addition to the tricritical and isolated critical points. The existence of compensation temperatures are also searched and it is found that the model gives two compensations for given system parameters.