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It was the sixth time Arsenal have scored five or more in a Premier League game this season without conceding and in such a tight race they now have a huge goal difference advantage which could prove crucial to the outcome.
Arsenal lead on 74 points, one point ahead of Manchester City.
Silva sidefooted the ball home in the 84th minute after Chelsea goalkeeper Djordje Petrovic parried a shot from former Blues midfielder Kevin De Bruyne.
City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat.
The heavy defeat leaves Everton 16th on 27 points, two places and two points above the relegation zone.
Juergen Klopp's side have 70 points from 30 games, two ahead of Arsenal and three more than champions Manchester City.
Van Dijk rose high above his marker to head a corner back across goal and into the far corner in the 118th minute.
Liverpool's patched-up side came out after the break in top gear.
Bayern CEO Jan-Christian Dreesen said there would a 'a new direction' next season with a new coach.
Manchester: Erling Haaland erased any questions about his scoring touch on Tuesday, netting Manchester City's only goal in a 1-0 victory over Brentford that lifted them into second place in the Premier League table, just one point behind leaders Liverpool. Pep Guardiola's team, unbeaten in their