By employing effective-field theory with correlations, the effects of exchange couplings and anisotropies on the physical properties of graphyne-like sandwich structure with a mixed-spin (5/2, 2) were analyzed. The various characteristic curves of the hysteresis loops, magnetization, susceptibility, internal energy, specific heat, as well as phase diagram was obtained. We found the multiple-loop hysteresis behaviors and reentrant phenomenon under certain conditions. Moreover, we also depicted the variation curves of dynamic magnetization under the impact of a periodically oscillating magnetic field. It is shown that a time-dependent and independent magnetic field can control and induce the disorder and order of the system.