This article presents the velocity and singularity analysis for a five-degree-of-freedom (5-DOF) parallel-serial manipulator. The hybrid structure of the manipulator combines a tripod-like parallel part and a serial part, represented as two carriages moving in perpendicular directions. This manipulator provides its end-effector with a 3T2R motion pattern, which includes three independent translations and two independent rotations. First, the study briefly discusses the manipulator design and the results of the position analysis. These results form the basis for the subsequent velocity and singularity analysis, performed by screw theory. The screw coordinates of the unit twists are written for each manipulator joint, and then through the reciprocal screw approach, the actuation and constraint wrenches of the manipulator are obtained by simple inspection. Based on these twists and wrenches, the paper forms the velocity equation and shows an example of the inverse velocity analysis for a given end-effector trajectory. The same example is solved by numerical differentiation to verify the proposed approach. Next, the paper investigates singular configurations by analyzing the wrench system of the manipulator and presents several conditions for serial and parallel singularities. Each condition has both a symbolic representation, given by an equation for screw coordinates of certain wrenches, and a visual representation, which shows the manipulator in a singular configuration.