After a 90 minute delay due to a technical glitch, the Carabao Cup announced that the draw had been pre-recorded.
And in the video posted on their Twitter account, Championship side earned the glamour tie of the round with Manchester United set to visit Ashton Gate.
Arsenal host West Ham, who staged a remarkable comeback against Spurs on Wednesday night.
Chelsea take on Bournemouth at Stamford Bridge while Premier League leaders Manchester City travel to Leicester.
All ties will be played the week commencing Monday December 18.
Fifth-round draw
Chelsea v Bournemouth
Arsenal v West Ham
Leicester v Manchester City
Bristol City v Manchester United