In the present study, hot deformation behavior of a FCC high-entropy alloy CoCuFeMnNi has been investigated to explore the stress–strain response for a wide range of temperatures and strain rates. The deformation response has been examined by plotting a processing map and examining the evolution of microstructure and texture in each of the temperature–strain rate domain. Hot compression tests were carried out in the temperature range 850–1050 °C at strain rates varying from 0.001 s−1 to 10 s−1. Stress–strain curves indicate characteristic softening behavior due to dynamic recrystallization (DRX). DRX has been observed along grain boundaries, shear bands, as well as in the interior of deformed grains. The size of dynamically recrystallized grains shows a strong dependence on deformation temperature and increases with temperature. A high degree of twin formation takes place in the DRX grains evolved inside the shear bands, and the extent of twinning decreases at high temperatures. The optimal processing window has been estimated based on strain rate sensitivity and has been validated with detailed analyses of microstructure and texture. The best region for thermo-mechanical processing has been identified as in the temperature range 850–950 °C at strain rate 10−1 s−1.