Jurgen Klopp’s side ran riot in the 202nd meeting of English football’s biggest rivals.
Naby Keita and Diogo Jota put Liverpool two goals ahead early on before Salah turned on the style with his treble.
United played most of the second half with 10 men after Paul Pogba was sent off in a chastening afternoon for Ole Gunnar Solskjaer’s team.
It was Liverpool’s biggest ever win at Old Trafford and their largest success against their old foes at any venue since 1925.
“I think it is great to win 5-0 here, we knew before the game it would be tough if we did not play our game,” Salah said.
“We knew they will come and try to give everything so we had to give 100 percent.
“We just tried to play our football and play in between the lines to create more chances. We did that and were lucky to score.
“As long as the team keep winning I am happy and to give my best to the team to win. The first goal I gave to Naby Keita to score.”
Salah is the first away player to score a treble at Old Trafford since Brazil legend Ronaldo in 2003.
He also became the highest scoring African player in the history of the Premier League with 107 goals, three more than Didier Drogba.
The 29-year-old has now scored in 10 successive games in all competitions, while Liverpool are unbeaten in their last 22 games in all competitions.
Liverpool are second, just one point behind leaders Chelsea, and look poised for a sustained assault on the English title currently held by Manchester City.
“We know what it takes to win the Premier League, we did it two years ago. A big win here but still only three points,” Salah said.
“We try to win each game and try to win the title. We need to play to win everything. From our heads from pre-season, we need to win the Premier League and hopefully we go for that.
“After half-time we were talking in the dressing room to just keep going and score as many as we could.”
Solskjaer hanging on
Meanwhile, Solskjaer said he has come “too far” as Manchester United manager to give up now, but the 5-0 thrashing yesterday left the Red Devils back where the Norwegian’s reign began.
Jose Mourinho was sacked in December 2018 following a 3-1 defeat at Anfield that left United sixth in the Premier League table.
A run of one point from a possible 12 has Solskjaer’s men down in seventh and already eight points off the race for the title after just nine games.
So much more was expected when United added Cristiano Ronaldo, Jadon Sancho and Raphael Varane to a squad that had finished second in the Premier League last season.
Rather than take the next step to challenge Chelsea, Liverpool and Manchester City for a first title since 2013, United have in Solskjaer’s own words “hit a brick wall”.
Now the club’s unpopular owners have a tough decision to make.
Liverpool’s last visit to Old Trafford was postponed in May as fans protested against the Glazer family in the wake of the failed European Super League project.
Ronaldo’s return headlined a £130 million ($179 million) investment in the transfer market to quell the disquiet towards the Glazers.
But their decision to hand Solskjaer a new three-year contract in July looks worse with every passing week.
Solskjaer is yet to win a trophy as United boss, but has been credited with finishing in the Premier League top four in consecutive seasons for the first time since Alex Ferguson retired as manager in 2013.
“I have come too far, we have come too far as a group. We are too close to give up now,” Solskjaer said defiantly as he fended off persistent questions over his future.
However, the 48-year-old recognised United have hit “rock bottom” given the context of a record home defeat to their fiercest rivals.
“This has been a monstrous day for Manchester United,” said former United captain Gary Neville. “They have been obliterated. That was unacceptable.”
A ex-teammate of Solskjaer’s, Neville has been criticised along with several other United legends for failing to criticise his management of a star-studded squad.
Even that shield for Solskjaer is now slipping as Neville joined Paul Scholes in questioning how much longer United can limp along without making a change.
“The pressure after this game is going to be intolerable in some quarters,” added Neville.
“The board have made everyone aware that they are steadfast in their support of the manager and that he stays. Results like this undermine that, there’s no doubt. This is sobering.”
To his credit, Scholes foresaw what was to come. In the aftermath of a dramatic 3-2 win over Atalanta in the Champions League on Wednesday, having trailed 2-0 at half-time, the former England midfielder said Liverpool would be four to the good by the break if afforded the same space.
So it proved as United went in at half-time 4-0 down for the first time in Premier League history.
Five minutes into the second period, it was 5-0 as Mohamed Salah completed a stunning hat-trick.
Liverpool arguably did not even make the most of a historic day as they played out the final 30 minutes with a man advantage after Paul Pogba’s red card without adding to the score.
“Ole’s at the wheel” rang out for the majority of the second half, but far from a show of support, it came from the small band of Liverpool fans mocking the United boss in celebration.
Many United fans had already exited Old Trafford. How long it takes for Solskjaer to be shown the door is now the question.