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England openers Rory Burns and Joe Denly put on nine runs in the fading light to extend the lead to 78 runs by the close of play for the day.
"If we can get a big lead, we can put some pressure on in the second innings," England's Sam Curran told Sky Sports after the match.
Archer took his tally for the series to 22 wickets, becoming the first England bowler to take two six-wicket hauls in an Ashes series since Ian Botham in 1981.
Left-armer Curran took two wickets in two balls on his way to a three-wicket haul and Chris Woakes claimed the prize scalp of Australian batting machine Steve Smith, who scored 80.
Australia are bidding to secure a 3-1 series victory after retaining the Ashes by winning the fourth test at Old Trafford, meaning England can at best only level the series 2-2.
Batsman Marnus Labuschagne said Australia wanted to win the series outright despite their relatively poor performance on Friday.
"The intensity definitely has not dropped. It's hard to say that when our play on the field maybe reflects that. But we came to win the Ashes and we really want to do that," he told BBC radio.
"We don't want to just retain the Ashes. We have to come out tomorrow 100% on and ready to take any chance."
England added just 23 runs to their overnight score of 271 before losing their last two wickets within half an hour in the morning. Australia's Mitchell Marsh claimed his first five-wicket haul in test cricket to end the innings.
Smith, who has scored more than twice as many runs as any other batsman in the series, underpinned the visitors' reply with more than four hours at the crease before being trapped lbw by Woakes to record his lowest score of the series.
He built his innings cautiously, scoring nine fours and just one six, which came when he lofted a Jack Leach ball far over long on to bring up his half-century.
It was Smith's 10th consecutive 50 against England in tests, the most in a row by any batsmen against any other nation in the longest format of the game.
Smith has now scored 751 runs in six innings, more than twice as many as any other batsman in the series.
Australia's openers David Warner and Marcus Harris both fell early in the day to the fast bowling of Archer for single-digit scores.
Warner's miserable series with the bat continued when, after picking up five runs, he got the slightest of touches on an Archer delivery as it flew through to wicketkeeper Jonny Bairstow.
Warner is the first opening batsmen in test cricket to get out for eight single-digit scores in a series, with only one innings left to play to get his Ashes average into double figures.
Archer claimed his second wicket soon after when Harris, on three, edged a ball to Ben Stokes at second slip.
England then struggled to break the combination of Smith and Labuschagne for almost an hour after lunch before Archer made the breakthrough, catching Labuschagne out lbw on 48 with an inswinging ball.
Curran then claimed the wicket of Matthew Wade, out lbw for 19 runs.
Marsh was out soon after tea, hooking an Archer bouncer all the way down to deep fine leg, where Leach crouched down in front of the boundary rope to take a low catch.
Curran stole Archer's limelight when he bagged the wickets of Australia captain Tim Paine (1) and Pat Cummins (0) with consecutive balls to leave the visitors on 166 for 7.
Archer then seized it back, claiming his fifth and sixth wickets of the day, those of Nathan Lyon (25) and Peter Siddle (18) - caught brilliantly by a diving Burns in the slips - to end the innings.