Ten years after Manchester City’s infamous 6-1 victory at Old Trafford, Liverpool inflicted one of the most embarrassing losses United have ever suffered.
It was Liverpool’s biggest win against United since 1925 and moved them seven points clear of Solskjaer’s side in the Premier League table.
Second-placed Liverpool are just one point behind leaders Chelsea as they chase the title — an ambition which looks completely beyond hapless United after this wretched afternoon.
“It is not easy to say something apart from it is the darkest day I have had leading these players,” Solskjaer said.
“You can look at last season when we lost to Spurs 6-1, but this is miles worse for me as a Manchester lad.”
In a telling indictment of United’s capitulation, thousands of fans left Old Trafford well before full-time.
United are languishing in seventh place after a fourth successive league game without a win, a dismal streak that includes three defeats.
The pressure on Solskjaer will be intense in the coming days as the beleaguered Norwegian faces a fight to cling onto his job.
“It is going to be a difficult one. We know we are rock bottom, we can’t feel any worse than this,” Solskjaer said.
“I have come too far, we have come too far as a group. We are too close to give up now.”
Liverpool boss Jurgen Klopp vowed to toast the “insane” rout with a beer or two on the way home from their largest ever win at Old Trafford.
“5-0, I couldn’t be happier, it is exceptional. Absolutely outstanding,” Klopp said.
“I have a few defeats in my mind which were not necessary but we won today so we drink beer on the way home!”
Liverpool have scored three or more goals in each of their last eight away games in all competitions.
“The result is insane, I asked if there was one like this in history and if there isn’t then it will take a while,” Klopp said.
“The players put a nice piece in the book. It is special but we don’t celebrate like crazy.”
They were ahead after less than five minutes when Salah played through Naby Keita, who slotted home in front of the shell-shocked Stretford End.
Liverpool smelt blood and grabbed a second in the 13th minute when Harry Maguire and Luke Shaw got in a tangle, allowing Trent Alexander-Arnold to cross for Diogo Jota to convert from close range.
Klopp’s side were rampant and Salah finished off Keita’s cross in the 38th minute.
With United in disarray, Maguire was pulled out of position and Salah struck at the far post in stoppage-time.
Salah was not finished yet and he ran clear to complete his treble in the 50th minute, making him Africa’s all-time leading scorer in the Premier League with 107 goals.
The Egypt forward had netted for the 10th successive game in all competitions and was the first away player to score a hat-trick at Old Trafford since Brazil legend Ronaldo in 2003.
Summing up United’s plight, France midfielder Paul Pogba, sent on at half-time, lasted just 15 minutes before being dismissed for a reckless studs-up lunge on Keita.
Liverpool are now unbeaten in their last 22 matches in all competitions, the kind of consistency that United can only dream about.
At the London Stadium, a second-half strike from Michail Antonio gave West Ham their second successive league win and condemned Tottenham to a second consecutive 1-0 loss this week.
Beaten by Vitesse Arnhem in the Europa Conference League on Thursday, Tottenham once again failed to produce a cohesive display as West Ham climbed above them into fourth place.
West Ham made the breakthrough in the 72nd minute as Antonio evaded Kane and poked home from Aaron Cresswell’s corner, making it 10 goals in 10 games against Tottenham for the striker.
In Sunday’s other match, Leicester won 2-1 at Brentford.
Youri Tielemans and James Maddison scored for Leicester either side of Mathias Jorgensen’s equaliser.