Multiphase Machines offer a promising solution to many practical challenges due to their advantages over the three phase counterparts, as fault-tolerant capability and lower torque ripple magnitude. Among different multiphase machines, five-phase machines correspond to a relatively practical selection in industrial applications. Multiphase machines are conventionally fed from voltage source inverter (VSI) as it facilities the operation under open-phase condition but with a sophisticated controller. Among different power converter topologies, current source inverter (CSI) features a simple inverter structure, a lower switching dv/dt, and a reliable short circuit protection. However, the control of multiphase CSI under open phase has not been yet considered in the literature. Additionally, the space vector PWM (SVPWM) of multiphase CSI is still challenging. Alternatively, the mapped sinusoidal PWM can offer simpler control over SVPWM. In this paper, a fault-tolerant controller for a five-phase CSI inverter is introduced and proposed for medium voltage drive applications. The proposed gating signal generator provides a controllable linear modulation index with the availability of over modulation. To verify the proposed fault-tolerant gating signal generator, a five-phase CSI feeds a static R-L load is simulated using MATLAB/SIMULINK as a case study exploring the healthy and the opened-phase cases.