Using the Monte Carlo method, we have studied the effect of the Hamiltonian parameters (the exchange couplings, the crystal and the magnetic fields) on the magnetizations, the phase diagrams and the hysteresis behavior of a hexagonal ferromagnetic or ferrimagnetic Ising core/shell nanoparticle with mixed spin-5/2 and spin-2. Interesting phenomena have been shown. In particular, the system exhibits the first order transition, the compensation temperature and the compensation crystal field. In addition, the nanoparticle presents single, double, triple and quintuple hysteresis loops.