Multi-phase ac motor drives are nowadays considered for various applications, due to numerous advantages that they offer when compared to their three-phase counterparts. In principle, control methods for multi-phase machines are the same as for three-phase machines. Variable speed induction motor drives without mechanical speed sensors at the motor shaft have the attractions of low cost and high reliability. To replace the sensor, information of the rotor speed is extracted from measured stator currents and voltages at motor terminals. Vector-controlled drives require estimating the magnitude and spatial orientation of the fundamental magnetic flux waves in the stator or in the rotor. Open-loop estimators or closed-loop observers are used for this purpose. They differ with respect to accuracy, robustness, and sensitivity against model parameter variations. This paper analyses operation of a Model Reference Adaptive System (MRAS)-based sensorless control of vector controlled five-phase induction machine with current control in the stationary reference frame. A linear neural network has been then designed and trained online by means of PI controller algorithm. The RNN-MRAS-based sensorless operation of a three-phase induction machine is well established and the same principle is extended in this paper for a fivephase induction machine. Performance, obtainable with hysteresis current control, is illustrated for a number of operating conditions on the basis of simulation results. Full decoupling of rotor flux control and torque control is realised. Dynamics, achievable with a five-phase vector controlled induction machine, are shown to be essentially identical to those obtainable with a three-phase induction.