Hall thruster is a kind of plasma optics device, which is used mainly in space propulsion. To simulate the discharge process of plasma and the performance of a 5 kW hall thruster, a two-dimensional PIC-MCC model in the R-Z plane is built. In the model, the anomalous diffusion of the electrons including Bohm diffusion and near-wall conduction is modeled. The Bohm diffusion is modeled by using a Brownian motion instead of the Bohm collision method and the near-wall conduction is modeled by a secondary electron emission model. In addition to the elastic, excitation, and ionization collisions between electrons and neutral atoms, the Coulomb collisions are included. The plasma discharge process including the transient oscillation and steady state oscillation is well reproduced. First, the influence of the discharge voltage and magnetic field on the steady state oscillation is simulated. The oscillation amplitude increases as the discharge voltage gets larger at first, and then decreases. While the oscillation amplitude decreases as the magnetic field gets stronger at first, and then increases. Later, the influence of the discharge voltage and mass flow rate on the performance of the thruster is simulated. When the mass flow rate is constant, the total efficiency initially increases with the discharge voltage, reaches the maximum at 600 V, and then declined. When the discharge voltage is constant, the total efficiency increases as the mass flow rate rises from 10 to 15 mg/s. Finally, a comparison between simulated and experimental performance reveals that the largest deviation is within 15%, thereby indirectly validating the accuracy of the model.