This work proposes the application of model predictive control (MPC) to the control of five-phase voltage source inverters. The additional switching states and degrees of freedom present in multiphase inverters increase the number of calculations in the predictive control algorithm making difficult to implement optimization problem online. In this paper a method to reduce the calculations is proposed. MPC prove to maintain the same simplicity and effectiveness as for three-phase converters. The successful performance of the proposed method of control for five-phase converters is verified by simulation.