In order to realize low energy consumption and smooth operation of the parallel mechanism driver, the dynamic load distribution of a spherical 5R parallel mechanism was optimized. First, the positive and negative solutions of the kinematic equation were deduced by the vector method. Then, considering gravity, the external force, and the inertial force of each component, the dynamic model of the spherical 5R parallel mechanism was established using the Lagrange method and the virtual work principle. A dynamic numerical simulation of the mechanism of this process was carried out. The results indicate that the maximum error of the theoretical value and simulation value is 1.3%, which verifies the correctness of the dynamic model. Subsequently, the multi-objective optimization function of the mechanism was established considering additional objectives, based on the dynamic model. In this regard, the power, torque, and the B spline interpolation method were used to plan the trajectory of the moving platform. The optimal trajectory of the actuator was determined using the normalized weighted-sum approach. Finally, the feasibility of the optimization method was verified using a numerical example. The results indicate that the peak amplitude of the power is 11.77% and 48.75%, the peak moment is 0% and 51.17%, and the peak velocity is 20.97% and 8.1%. Based on these results, the peak output value of the actuator can be effectively reduced using the optimization method, so that the output of the parallel mechanism driver is more stable. This optimization method of dynamic load distribution is also practical for use in other parallel mechanisms.