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Experimental results reveal that the apparent activation-energy for grain-growth in an fcc-based AlxCoCrFeNi high entropy alloy (HEA) system increases from 179 to 486 kJ/mol when the Al content increases from x = 0.1 to 0.3. These unexpectedly high apparent activation-energy values can be potentially attributed to solute clustering within the fcc solid-solution phase that develops with increasing Al content in this HEA. Detailed microstructural analysis using atom-probe tomography and density functional theory (DFT) calculations strongly indicate the presence of such nanoscale clusters. This phenomenon can change grain-growth from a classical solute-drag regime to a much more sluggish cluster-drag based mechanism in these HEAs.