Driving system parameter optimization (DSPO) is an important approach to improve robots' dynamic performances such as acceleration capacity, load carrying capacity, and operation stability. To achieve better dynamic performance, motors with high power and high cost are generally used. But this leads to a waste of resources. It is difficult to simultaneously make the robots satisfy the prescribed requirements and avoid over conservative design. This issue is much more challenging for parallel machining robots due to the coupling characteristics of the closed kinematic chains. In this paper, a 5 degrees-of-freedom (DoF) parallel machining robot with planar kinematic chains is presented, and its dynamic model is established based on the virtual work principle. Then, a DSPO method for 5-DoF machining robots is proposed by considering the classical machining trajectories that can reflect the robots' performance requirements. The motor output under these trajectories and candidate motor parameters are presented in a comprehensive graph. Combined with motor selection criteria, the feasible motors and usable reduction ratio range are derived. To optimize the reduction ratio, a dynamic index is proposed based on the variance degree of the motor output torque to evaluate driving system's operational stability. On this basis, the optimal reduction ratio is obtained by minimizing this index to improve the stability of machining robots. Based on the proposed method, the DSPO for the 5-DoF parallel machining robot is implemented, and the optimal driving units are generated. The proposed method can be used for the DSPO of other 5-DoF parallel machining robots.