Tool path planning of CNC motion controller includes tool path interpolation and velocity planning. Five-axis machine tools have been adopted in mold surface and aerospace part machining. In this paper, the kinematics frame based on dual quaternion D-H representation was applied to define the coordinates of five-axis machines systematically. Consequently, the kinematics parameter equation of the five-axis machine was obtained through this procedure. A new interpolation algorithm using quaternion-quintic spherical Bezier spline was proposed. Jerk Control, which automatically applied the appropriate amount of acceleration control that created smooth path transitions and consequently less mechanical stress on the machine. Therefore, in this paper, a novel interpolation algorithm with quadric jerk velocity profiles was proposed. The experimental results show the feasibility of proposed tool path planning for five-axis machining.