High-pressure torsion (HPT) is applied to a face-centered cubic CoCrFeMnNi high-entropy alloy at 293 and 77 K. Processing by HPT at 293 K produced a nanostructure consisted of (sub)grains of~50 nm after a rotation for 180 • . The microstructure evolution is associated with intensive deformation-induced twinning, and substructure development resulted in a gradual microstructure refinement. Deformation at 77 K produces non-uniform structure composed of twinned and fragmented areas with higher dislocation density then after deformation at room temperature. The yield strength of the alloy increases with the angle of rotation at HPT at room temperature at the cost of reduced ductility. Cryogenic deformation results in higher strength in comparison with the room temperature HPT. The contribution of Hall-Petch hardening and substructure hardening in the strength of the alloy in different conditions is discussed.