When face-centered cubic (FCC) metals and alloys with low stacking fault energy (SFE) are irradiated by high-energy particles or deformed at high speed, stacking fault tetrahedra (SFTs), which are a type of vacancy cluster defect, are often formed. Therefore, SFTs were expected to form in the CoCrFeMnNi equiatomic high-entropy alloy (HEA). However, no SFT was observed in the CoCrFeMnNi HEA with high-speed plastic deformation even after annealing at 873 K. To elucidate this mechanism, the binding energy of vacancy clusters in the CoCrFeMnNi HEA was calculated based on first principles. The binding energy of the di-vacancy cluster was positive (average of 0.25 eV), while that of the tri-vacancy cluster was negative (average of - 0.44 eV), suggesting that the possibility of formation of a tri-vacancy cluster was low. The inability to form a cluster containing three vacancies is attributed to the excellent irradiation resistance of the CoCrFeMnNi HEA. However, if an extra vacancy is added to a tri-vacancy cluster (with negative binding energy), the binding energy of the subsequent tetra-vacancy cluster may become positive. This suggests that it is possible to form vacancy clusters in the CoCrFeMnNi HEA when high-energy ion or neutron irradiation causes cascade damage.