[en] The magnetic properties of mixed spins-5/2 and -2 Ising model on the two alternative layers on a honeycomb lattice are investigated and are discussed using the Monte Carlo simulations. The different ground-state phase diagrams are found. The eight magnetic stable phases are obtained for a fixed magnetic parameters. The critical temperatures are deduced for different layers. The system exhibits the second order and first order phases transitions. The plateau obtained between the high temperature phase and low-temperature phase at critical temperature can be explain by first-order transition. The second order transitions also show continuity in order magnetization at the reduced critical temperatures. The variation of magnetizations with exchange interactions and crystal field in each layer has been given. Magnetic hysteresis cycle has been obtained for different layers, temperatures and crystal fields. (author)