The hot compressive deformation mechanism and processing maps of the equiatomic FCC CoCrFeMnNi high-entropy alloy (HEA) were studied in the temperature range between 1023 and 1323 K and in the strain rate range between 10−3 and 10 s−1. At high strain rates above 1 s-1, strain hardening was dominant even at the very high temperature of 0.84Tm, which may be attributed to the sluggish diffusion coefficient and low stacking fault energy of the CoCrFeMnNi HEA, leading to suppression of dynamic recovery. According to the processing maps, the best condition for hot working was near 10−3 s−1 at 1323 K. Power-law breakdown and unstable flow occurred at low temperatures and high strain rates where the strain hardening was pronounced. The activation energy for plastic flow measured in the power-law creep regime when considering the dependence of elastic modulus on temperature was 312.2 kJ/mol; this value is close to the activation energy for the weighted diffusion coefficient calculated by weighting the contribution of each element in the CoCrFeMnNi HEA (284 kJ/mol). The size and fraction of the dynamically recrystallized grains increased as the strain rate decreased and the temperature increased, as in conventional metals. Both discontinuous dynamic recrystallization and continuous dynamic recrystallization (CDRX) occurred. CDRX became more distinct as the temperature increased. The deformation mechanism and behavior of the CoCrFeMnNi HEA were very similar to those of FCC pure metals in terms of the stress exponent and the effect of the stacking fault energy and diffusivity on the creep rates.