Additive manufacturing (AM) has gained significant attention in academia and industry over recent decades. Two inherent challenges faced by conventional three-axis printing are the staircase effect and the need for support structures for overhangs. The emerging multi-axis AM introduces a novel printing process with a variable build direction, offering potential solutions to mitigate these issues. In this study, we develop an extrusion-based five-axis Fused Deposition Modeling (FDM) AM system, concentrating on the implementation of cutting-edge multi-axis printing strategies. We present a collection of algorithms, encompassing the 3+2-axis printing pipeline and the five-axis sculpture printing, to demonstrate the feasibility and versatility of our system. The findings reveal that our system can achieve support-free printing of intricate components with enhanced surface quality and curved layer sculpting with variable depth, while simultaneously reducing both printing time and material consumption.