We present a postprocessing algorithm for 5-axis machines, which can be applied to types with two rotary axes (2R-3L) and three rotary axes (3R-2L). Five-axis machining requires a postprocessor for converting cutter-location (CL) data to numerical-control (NC) data. The existing methods for postprocessing use inverse kinematics equations from the forward kinematics. However, for 5-axis machines with three rotary axes, the inverse kinematics equations cannot be induced directly, because the forward kinematics equations are coupled. To derive the joint values from the forward kinematics equations, previous algorithms use iterative numerical methods for the postprocessing; this requires a search algorithm with much computation time and may fail to obtain a solution. Our algorithm has three advantages: first, the forward kinematics equations are not required; second, the method is reliable and eliminates the need for numerical methods for the inverse kinematics, which results in exact solutions; and finally, the proposed algorithm is generic for 5-axis machines, which can also be applied to 2R-3L 5-axis machines.