Torque density is usually improved by injecting the third current harmonic for five-phase permanent magnet synchronous machine (PMSM). It increases the degrees of freedom of a multiphase drive. However, it also separates the current limitations of the motor and the transistors, respectively related to the RMS and peak values of the currents. These two constraints are represented by Maximum Torque Per Ampere (MTPA) strategy and Maximum Torque Per Peak Current (MTPPC) strategy. In this paper, these two strategies are studied and analyzed in order to optimize the generated torque with injection of the third current harmonic. Torque improvement principle and the optimizing algorithm considering two constraints are illustrated. Then, the analytical results of these two strategies are compared and discussed. It is shown that injecting the third current harmonic can improve the torque especially at flux-weakening region. Besides, compared with MTPA, MTPPC could produce higher torque for the same inverter current limit.