The five-degree-of-freedom (5-DOF) magnetic levitation bearing control system, composed of two radial bearing units and one axial unit, is a multivariable, nonlinear, and inherently unstable system. Building upon an existing four-DOF experimental platform, this paper designs an axial bearing and establishes a mathematical model for the 5-DOF system. To address the inherent nonlinearity, strong coupling, and instability of magnetic levitation systems, this paper integrates the actual rotor motion states to achieve decoupling of the 5-DOF system and linearization of electromagnetic forces. Based on the refined model, a Model Predictive Controller (MPC) is explicitly designed. Simulation experiments demonstrate that the designed MPC controller, without requiring extensive parameter tuning, significantly outperforms conventional PID controllers in magnetic levitation systems by enhancing both transient performance and robustness.