City boss Pep Guardiola, who has reached the semi-finals of the Champions League in each of the last seven seasons as a manager and has won it in 2009 and 2011, faces a stern test against the Ligue 1 leaders.
Sergio Aguero, in Guardiola's doghouse, scored too goals and set up Leroy Sane for the fifth.
More importantly than any of that they have one of the best managers in the world in Guardiola, Champions League victor in 2009 and 2011.
Even after rather fortunately drawing level and making another mistake to gift Monaco a 3-2 lead - though Falcao's finish was nothing short of exceptional - City still rolled up their sleeves and dug in.
"We work hard to put on a show", said Jardim, whose team have now scored 111 goals in all competitions this season and are the top scorers in Europe's five top leagues. "We were stable mentally", he said.
Free-scoring Monaco have smashed in an incredible 76 goals in 26 league games this season boasting some exciting young talent along with a rejuvenated Radamal Falcao.
Stones, who scored his first Champions League goal, reflected on "great team spirit, great desire and great goals from us". "It makes the team much better", Toure continued.
"I am really impressed how good they are", said Guardiola. Guardiola's squad flew to Abu Dhabi after the game for warm-weather training, with the manager adding: "I am satisfied it is 5-3 because we could be sat here out of the competition because the line was so fine". "We will see after the session tomorrow". I've got the right people around me here and feel like I'm going in the right direction.
Since the inception of the Champions League, there have been 19 group stages games with at least eight goals In addition to the six eight-goal contests in the knockout rounds.
Pep Guardiola said after the game: "I'm so happy for the result because we're still alive, and especially for the performance of the guys. We know there's lots of space in behind", the Portuguese told his post-match press conference.
"We've still got 90 minutes to play and it's far from over".
'That is why they wanted me to come here - I love to play in that way, I think it is something special when two teams play in that way, attack and attack.
Auguero was then sensationally yellow-carded after being fouled by Subasic in the box as he looked to round the keeper, while Mbappe blazed over as the action immediately swung to the other end following a long ball forward from the keeper.
This proved the turning point of the game and the crowd lifted to get behind their team, in protest of the decision.