A discrete mathematical model of a permanent magnet synchronous motor (PMSM) is established, then the fifth-order cubature Kalman filter (CKF) algorithm is introduced. A Gauss–Newton iterative method is introduced into the iterative process of the fifth-order CKF algorithm to generate the innovation variance and covariance. Therefore, an iterative fifth-order CKF algorithm is proposed as the basis of a PMSM sensorless control is implemented. Then, a PMSM sensorless control based on the iterative fifth-order CKF algorithm is applied to an electric power steering (EPS) system, whose control system is constructed by adopting the typical assist and return control strategy. Finally, to verify the performance of the proposed PMSM sensorless control method, the EPS system model of the PMSM sensorless control is built by using the common phase-locked loop (PLL), the CKF algorithm, the fifth-order CKF algorithm, and the proposed iterative fifth-order CKF algorithm. The simulation analyses and the experimental tests show that the proposed iterative fifth-order CKF algorithm can estimate the PMSM speed with good accuracy and has a strong resistance to disturbances in the load and speed. The assist and return performances of the EPS system are also improved.