The work aims to study the workspace of 5R parallel mechanism in different assembly and working modes, and provide theoretical support for the workspace analysis and path planning of the mechanism similar to 5R planar mechanism. The singular matrix of kinematics was obtained by deriving the constraint equation. The workspace boundary constraint equations were established and the constraint inequations were built based on the definition of assembly and working modes. The workspace image of 5R parallel mechanism in different assembly and working modes was obtained. The union of the workspaces corresponding to assembly mode “+−” was the reachable workspace. According to the combination of assembly and working modes, eight different workspaces could be obtained. Cylindrical Decomposition in solving the problem of workspace has certain application value. The set of inequalities are solved with Mathematica, and the results are intuitive and easy to understand.