5-axis machining is widely used to manufacture complex sculptured parts, such as impellers used in jet engines. In order to machine complex part surfaces, the surface is discretized by a series of short-segmented point to point linear segments by CAD/CAM systems. Smooth non-stop motion of the tool must be interpolated along those discrete tool-paths. This paper proposes novel discrete linear path smoothing algorithms to interpolate tool position and orientation commands synchronously for 5-axis machining. Finite Impulse Response (FIR) filtering based feed profiling technique is developed to generate a smooth tool-pose trajectory with both local and global smoothing functionality. Analytical techniques are proposed to confine the blending errors within user specified tolerances. The proposed technique is computationally efficient and suitable for real-time implementation on modern NC systems. Path blending errors are defined in both the Cartesian workpiece coordinate system for tool positioning errors and the spherical coordinate system for tool orientation errors. Both position and orientation contouring errors are controlled in each coordinate system with respect to the user-defined tolerances. Simulation results validate that the proposed FIR based corner smoothing algorithm can generate smooth and non-stop trajectories for 5-axis machining. It can lead to significant cycle time gain without jeopardizing part tolerances.