Pep Guardiola's men made a blistering start, taking the lead inside ten minutes through Mahrez, who calmly finished from Kevin de Bruyne's pass.
City kept their foot on the gas and doubled the lead after 17 minutes, as Bernardo sensationally found the net via the crossbar.
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The superb start continued, with Foden adding a third from close-range after neat work on the right flank by Mahrez just after the half hour mark.
Just before the interval, Bernardo added City's fourth of the evening as his sweeping shot deflected beyond the helpless Sporting goalkeeper Adan.
The Portuguese had the ball in the net a third time only to be denied for offside after a VAR check after the break, but the fifth goal did arrive shortly after, with Sterling curling sumptuously into the top corner.