A spatial parallel kinematic mechanism (PKM) with five degrees of freedom (DoFs) and three limbs is proposed in this paper. To investigate the characteristics of the proposed mechanism's DoFs, mobility analysis based on a line graph method and Grassmann line geometry is carried out. The results show that the mobile platform can rotate about a fixed point at the base and translate in a specific plane (i.e., three rotations and two translations). Therefore, the mobile platform can be located at an arbitrary point in the space and has flexible orientational capability. The orientation of the mobile platform is described by using tilt-and-torsion (T&T) angles, and the kinematics model is established with this precondition. Within the process of kinematics modeling, parasitic motion of the mobile platform is analyzed, and singularity configurations are also disclosed. On this basis, four working modes with different configurations are identified, and one of them is focused on and investigated in detail. The proposed PKM has good potential to be used in the development of movable machine centers. The kinematic analysis is very helpful for the understanding of the concept and the potential applications.