This paper presents a speed sensorless control of a five-phase PMSM in healthy operation and under the Open-Phase Fault on any phase of the machine. The solution is recommended for mission-critical applications requiring high reliability capacities, such as Aerospace applications. An adapted Active Fault Tolerant Control is proposed with the aim of obtaining electromechanical torque as close as possible to that normally developed by a machine working in healthy condition. In instances of a loss of power to one phase of the machine, a reconfiguration of the control law is performed to ensure the continuity of service and to maintain acceptable control performances without requiring a hardware rearrangement of the power architecture. The motor rotation speed and position, required for the Field Oriented Control (FOC) of the stator currents, are estimated using a Back-Electromotive Forces (Back-EMF) observer based on a mathematical model of the motor and implemented in the stator diphase reference frame. Different electrical models that describe the behavior of the five-phase machine in the normal and degraded operations are given. Experimental results on a 1.25 kW synchronous PM machine are shown to confirm the effectiveness of the motor control.