This study proposes two flux-weakening control strategies for a new five-phase fault-tolerant interior-permanentmagnet (FT-IPM) motor, in which direct torque flux-weakening control (DTFWC) and space vector pulse width modulation (SVPWM)-based vector flux-weakening control (SVMFWC) are adopted. To achieve the reduced computation and the good operating performance such as minimised copper loss, improved dynamic response performance, and constant power operation in FW region, the multi-objective optimisation without complex non-linear optimisation algorithms for the DTFWC and SVMFWC are developed. In addition, the two proposed strategies have the same control objective but realised with two different ways. The reducing copper loss is obtained in DTFWC by reducing flux-weakening current with the full utilisation of DC-link voltage, while the reducing copper loss is gained in SVMFWC by decreasing the required current amplitude with maximum output torque per ampere current. Furthermore, the effectiveness of the proposed DTFWC and SVMFWC strategies is verified by simulation and experimental results.