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Using the Monte Carlo method, we have examined in detail the thermal and magnetic properties of a ferrimagnetic mixed-spin (3/2, 5/2) hexagonal Ising nanowire with a core-shell structure. Under the effects of single-ion anisotropy and exchange couplings, we examined different magnetic properties such as partial and total magnetization, susceptibility, specific heat, and phase diagrams. Our particular results show that the system exhibits the second-order phase transitions as well as the compensation points for certain conditions. Moreover, the multiple hysteresis loops with various shapes and step effects have been detected. These important phenomena are compared with previous theoretical and experimental studies. [ABSTRACT FROM AUTHOR]