Multi-phase motors are gaining more attention due to the advantages of good fault tolerance capability and high power density, etc. By applying dual-rotor technology to multi-phase machines, a five-phase dual-rotor permanent magnet synchronous motor (DRPMSM) is researched in this paper to further promote their torque density and fault tolerance capability. It has two rotors and two sets of stator windings, and it can adopt a series drive mode or parallel drive mode. The fault-tolerance capability of the five-phase DRPMSM is researched. All open circuit fault types and corresponding fault tolerance techniques in different drive modes are analyzed. A fault-tolerance control strategy of injecting currents containing a certain third harmonic component is proposed for five-phase DRPMSM to ensure performance after faults in the motor or drive circuit. For adjacent double-phase faults in the motor, based on where the additional degrees of freedom are used, two different fault-tolerance current calculation schemes are adopted and the torque results are compared. Decoupling of the inner motor and outer motor is investigated under fault-tolerant conditions in parallel drive mode. The finite element analysis (FMA) results and co-simulation results based on Simulink-Simplorer-Maxwell verify the effectiveness of the techniques.