This work presents a 3UPS-2RPRRR parallel robot and its geometric analysis. The robot has three rotational degrees of freedom and two translational degrees of freedom in the XZ plane. The inverse geometric model was obtained by closed-loop analysis. The direct geometric model was obtained analytically by the representation of the geometrical varieties for each end limb. The intersection of varieties results in a multivariate nonlinear equation system. The nonlinear system was solved founding four assembly modes. We use the free package SageMath. Two solution methods were addressed: numerical one solution, and Gröbner basis with Toy Buchberger algorithm. Finally, example calculations of inverse and forward geometrical model were analyzed and plotted.