This paper describes an optimal torque per peak current control method for a five-phase permanent magnet (PM) machine considering both 3rd and 5th harmonic currents. These optimal ratios to the fundamental component are analytically derived to maximize the output torque. It is found that except for the 3rd harmonic current contributing to the output torque, the 5th harmonic current can also produce the additional positive torque. However, the 5th harmonic is zero sequence component for the five-phase machines, which does not exist in the phase windings. Hence, the neutral point is required to connect the middle point of the DC link capacitors for constructing flowing path. The conventional vector space decomposition (VSD) control is extended to zero sequence sub-plane, which can quantitatively control 5th harmonic current. For a prototype five-phase PM machine, the average torque can be increased by 21.4% with 3rd harmonic current injection. Meanwhile, 10.7% additional positive torque is achieved together with 3rd and 5th harmonic injection. The torque ripple remains similar to that without harmonics injection. Finally, the experiments are given to demonstrate the theoretical analysis.