In order to enhance torque density of five-phase permanent magnetic synchronous motor with third harmonic injection for electric vehicles (EVs) applications, optimum seeking method for injection ratio of third harmonic was proposed adopting theoretical derivation and finite element analysis method, under the constraint of same amplitude for current and air-gap flux. By five-dimension space vector decomposition, the mathematic model in two orthogonal space plane, $d_1-q_1$ and $d_3-q_3$, was deduced. And the corresponding dual-plane vector control method was accomplished to independently control fundamental and third harmonic currents in each vector plane. A five-phase PMSM prototype with quasi-trapezoidal flux pattern and its fivephase voltage source inverter were designed. Also, the dual-plane vector control was digitized in a single XC3S1200E FPGA. Simulation and experimental results prove that using the proposed optimum seeking method, the torque density of five-phase PMSM is enhanced by 20%, without any increase of power converter capacity, machine size and iron core saturation.