We studied an Ising ferromagnet on a bipartite square lattice with nearest-neighbor ferromagnetic exchange couplings between spin values SiA=2 and σjB=5/2, next-nearest-neighbor exchange couplings between spins, SiA=2 and an average term of single-ion anisotropy for each lattice site. We carried out Monte Carlo simulations on the planes (D′,kBT′) and (J2′,kBT′) to investigate the influence of exchange parameters J2′ and anisotropy of D′ lattice on the critical temperature of the system. The thermal behaviors of the sublattice magnetizations, total magnetization and specific heat were investigated. We found that the critical behavior system depends linearly on the next-nearest-neighbor interaction J2′ and for antiferromagnetic exchange interactions the system undergoes reentrant phenomena.