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The use of lower mobility parallel manipulators with less than six degrees of freedom (DOFs) has drawn a lot of interest in the area of parallel robots. In this paper, the type synthesis of 3R2T 5-DOF parallel mechanisms (PMs) is performed systematically using the Lie group of displacements, where R denotes a rotational DOF, and T denotes a translational DOF. First, some necessary theoretical fundamentals about the displacement group are recalled. Then, a general approach is proposed for the type synthesis of 3R2T 5-DOF PMs. The limb kinematic chains, which produce the desired displacement manifolds, are synthesized and enumerated. Structural conditions, which guarantee that the intersection of the displacement manifolds generated by the limb is the desired 5-DOF manifold, are presented. An exhaustive enumeration of 3R2T 5-DOF symmetrical PMs is obtained. Finally, an input selection method is proposed.