This paper presents a study of control strategies for 5-phase permanent magnet synchronous motors (PMSMs) supplied by a five-leg voltage source inverter. Based on the vectorial decomposition of the multi-phase machine, fictitious machines, magnetically decoupled, allow a more adequate control. In this paper, our study focuses on the vector control of a multi-phase machine using a linear proportional-integral-derivative (PID) current regulator in the cases of sinusoidal and trapezoidal back-electromotive force (EMF) waveforms. In order to determine currents’ references, two strategies are adopted. First one aims to minimize copper losses under constant torque, while the second one targets to increase torque for a given copper losses. These techniques are tested under a variable speed control strategy based on a proportional-integral (PI) regulator and experimentally validated.