Recent studies on Co–Cr–Fe–Ni–Nbx (x = molar ratio) high-entropy alloys (HEAs) have revealed that high-pressure torsion (HPT) induced severe straining improves the load-bearing ability of eutectic HEAs. Nanoindentation using a Berkovich indenter was employed to investigate the influence of severe straining on the rate-dependent strength responses in eutectic, proeutectic, and single-phase Co–Cr–Fe–Ni–Nbx HEAs. The results reveal that the nature of the microstructure evolution after severe straining significantly affects Young's modulus and the yield strength in eutectic Co–Cr–Fe–Ni–Nb0.65. The excellent combination of high strength with lower Young's modulus is crucial for opening new sights in lamellar eutectics for possible application as next-generation advanced materials.