Parallel mechanisms with linear moving platform (LMP) have good practical application value, but it was rarely studied. Firstly, using structure coupling-reducing theory based on the position and orientation characteristics (POC) and the ordered single-open-chain (SOC) units, five 5—SPS parallel mechanisms with LMP were designed, and four of them were novel ones. Secondly, the “existence criterion of mechanism” was proposed. Each 5—SPS parallel mechanisms with LMP had its own advantages and applications. Accordingly, the existence of five 5—SPS and the non-existence of 6—SPS, 4—SPS, 3—SPS, 2—SPS parallel configurations with LMP were proved. As a consequence, the criterion can be used to determine the existence of mechanisms. Then, the three important topological characteristics, including coupling degree, the output POC and the input-output motion decoupling, as well as the position workspace characteristics, of the five 5—SPS parallel mechanisms with LMP were separately calculated and compared. It was shown that the coupling degree of mechanisms and difficulty of solving forward displacement analysis can be reduced, but the workspace would be reduced simultaneously when the collinearing or coinciding of the spherical joints on the moving platform was occurred. And the mechanisms with triple-spherical-joint structure had input-output motion decoupling. These results can provide theoretical basis for engineering design, optimal selection and potential use of the five 5—SPS parallel mechanisms with LMP.