The remarkable scoreline represented United's biggest away win in Europe since a 6-1 demolition of Borussia Dortmund in 1964.
Only once have they won by a greater margin on their travels, when a Busby Babes outfit containing Bill Foulkes, who died earlier this week, defeated Shamrock Rovers 6-0.
It was the first time an English side had won by such a massive scoreline in Germany since the Champions League was launched in 1992.
Yet Moyes believes life can get better.
"It was one of my best days as Manchester United manager but the best days are still to come," he said.
"We won well and played well, with some outstanding performances.
"Bayer Leverkusen have a great record here so to come here and win 5-0 puts it into perspective as well."
Though Wayne Rooney did not get on the scoresheet, his name was stamped all over a classy display.
Rooney collected the first four assists and was off the pitch when Nani scored United's fifth.
It was his cross that provided Antonio Valencia with a first half tap-in and before he then curled over the free-kick that was headed into his own net by Emir Spahic as United took command before the break.
But the striker was not finished. His close-range shot midway through the second period was too hot for Bernd Leno to hold, allowing Jonny Evans to finish off and then he lobbed a pass to Chris Smalling for number four.
Little wonder Moyes said prior to the game he had no intention of tempering the 28-year-old's aggressive instincts.
And though the Scot feels Rooney may need a break at some point, it is not going to happen any time soon.
"Wayne does not need a rest just now but I will be watching for any sign he does," said Moyes.
"We need people in form and fit, so I want to keep him as fresh as I can.
"He is one of those players who is probably better playing, but I don't want to find myself losing him for five or six games somewhere in the season."
Nani completed the rout, with that goal created by Ryan Giggs, who excelled in his central midfield berth just two days short of his 40th birthday.
And though there is plenty of time to make a decision, the chances of him extending his stellar career for yet another season are increasing.
"People mention his age but all you should talk about is his fooball ability," said Moyes.
"He is an unbelievable footballer - and you could say he is getting better. His vision and pass for Nani's goal were fantastic.
"He is a wonderful player and I am really fortunate to be working with him.
"He will tell us when he has enough, or when he thinks his time is up. But his performances since I came have been excellent."
Moyes also had words of praise for Shinji Kagawa, who operated in his preferred role just behind central striker Rooney and was outstanding.
"Shinji played really well," he said.
If there was a minor blemish as United booked their last 16 spot with a game to spare, it came with Shakhtar Donetsk's victory over Real Sociedad.
It means United must get a point against the Ukrainian champions at Old Trafford in a fortnight to be certain of top spot in Group A, which would mean avoiding a hazardous knockout round encounter with one of Europe's heavyweights.
Leverkusen could still advance too. However, the shattering defeat - their first on home soil this season - will take some recovering from.
"Tonight we were taught a lesson," said boss Sami Hyypia. "Manchester United are a great counter-attacking side. If you go a goal behind against them you are in trouble."
Beaten at Old Trafford in September, Hyypia was asked whether his side had a psychological problem facing the Premier League champions.
"Yes," he said. "Maybe."
Source: PA
Source: PA