The accuracy and stability of robotic systems are significantly influenced by joint clearances, especially in precision applications like optical mirror polishing. This study focuses on a 5-DOF (Degree of Freedom) parallel manipulator designed for optical mirror polishing. The study conducts dynamic modeling by incorporating prismatic joint clearance and examines the resulting dynamic response. Previous studies on dynamic modeling have primarily focused on planar mechanisms with rotational or ball joint clearances, whereas research on parallel manipulators with spatial prismatic joint clearances remains limited. This study introduces a comprehensive dynamic modeling framework for parallel manipulators with prismatic joint clearance, utilizing the Lagrange multiplier method (LMD). First, the prismatic joint models of the guideway and slider in the parallel manipulator are simplified, enabling the determination of different contact states and the calculation of friction and contact forces for various contact types. Second, the dynamic equations of the parallel manipulator are derived by establishing system constraint equations. Finally, the dynamic responses of various clearance-related factors are determined through a combination of theoretical calculations and ADAMS simulations. This study provides a framework for modeling the dynamics of parallel manipulators with prismatic joint gaps, offering valuable insights into the design and control of high-precision robotic systems.