This paper introduces a novel method to achieve sensorless speed control of a Five-phase Permanent Magnet Synchronous Motor (PMSM) drive in case of a single-phase open-circuit fault regardless which phase is open. The motor performance when an open circuit fault occurs is as good as it is before the fault. The degradation in motor performance, when an open circuit fault occurs, is minimized due to implementing a novel control technique that is using the four remaining healthy currents. This strategy includes introducing two software modifications to the operation of the five motor post the fault. Firstly, an asymmetric SVPWM is used post the fault instead of multi-dimension SVPWM that is used before the fault. Secondly, a new algorithm is introduced to track the saliency post the fault. The new algorithm is considering the application of the new modulation technique. Moreover, it uses only the excitation in the healthy currents of the motor due to the IGBT switching actions. Simulation results presented in this paper shows that the performance of the motor over a wide speed range and at different load conditions is maintained post the fault.