We have demonstrated a 5 kW high-power monolithic fiber amplifier employing a homemade spindle-shaped ytterbium-doped fiber (YDF) based on the main oscillator power amplifier configuration. The YDF consists of a spindle-shaped core and cladding along the fiber length, with a core/cladding diameter of 27/410 µm at both ends and 39.5/600 µm in the middle. An output power of over 5 kW and beam quality of about 1.9 and an optical-to-optical conversion efficiency of 66.6% were achieved in the amplifier under a bidirectional pump scheme. While operating at the maximum power, the laser performance was evaluated, and the transverse mode instability and stimulated Raman scattering effects were well mitigated. To the best of our knowledge, this is the highest power demonstration in a continuous-wave fiber laser employing a tapered fiber. Further power scaling is promising by optimizing the structure of the YDF.