A six degrees-of-freedom (DOF) two-radii Gough–Stewart Platform (GSP) can be designed to be dynamically isotropic and has been proposed for micro-vibration isolation. In many applications, the torsional mode can be ignored, and a 5DOF dynamically isotropic, parallel manipulator capable of attenuating three translational (3T) and two rotational (2R) modes are sufficient. In this work, we present the designs of a novel 5DOF dynamically isotropic parallel manipulator for vibration isolation where the torsion mode can be ignored. We present closed-form solutions in their explicit form, and these are obtained using a geometry-based approach. The first design is based on a modification to the two-radii GSP and provides enhanced design flexibility and feasibility. The second design, with the first five decoupled modes, is based on superposing geometrical parameters of two three-legged dynamically isotropic or decoupled parallel manipulators. It is shown that this design has two translational modes, namely the X, Y modes, which are decoupled from two rotational modes Rot(X), Rot(Y) and are controlled by two different sets of three legs. This feature can lead to simpler control and less power requirements if active vibration control is chosen. The designs presented in this work include the effect of asymmetry and the payload center of mass variation. The dynamically isotropic and decoupled designs were successfully validated using the finite element software ansys®. Experimental results based on a two-radii GSP prototype further validate analytical and simulation results.