Julian Nagelsmann's Germany next face Hungary on Wednesday before taking on Switzerland in their final Group A match.
"We played with a lot of intensity and played the right spaces, took some risks and that is why we scored. We played an outstanding first half and we were up 3-0," Germany captain Ilkay Guendogan said.
"That is how we wanted to start. I had a good feeling before the game and I was proved right."
"The start is what we wanted but still the goal we let in showed that all teams have quality and if you don't pay attention you will be punished."
The Scots, who lost Porteous for a studs-up challenge on Guendogan that earned the hosts their penalty, must quickly go back to the drawing board and regroup if they are to make it past the group stage for the first time in a major tournament.
POWERFUL START
The Germans, who lost their opening matches at the 2018 and 2022 World Cups as well as the previous Euros in 2021, dominated possession from the start with the Scots defending high.
That ambitious strategy proved fatal for the visitors, who left far too many open spaces at the back, and it did not take long for the hosts to punish them.
Toni Kroos flighted a perfect 30-metre cross for Joshua Kimmich who timed his pass to Wirtz perfectly for the winger to drill home for a 10th minute lead and become the youngest scorer for Germany at a Euros aged 21.
With Scotland still recovering, Germany struck again nine minutes later, with Guendogan slipping another ball past the Scottish backline, this time for Havertz on the left, with the forward laying it off for Musiala in the box to rifle home.
It was the start all of Germany was hoping for as hundreds of thousands of supporters across several fan zones erupted with joy, but there was more to come with Porteus' reckless challenge and dismissal conceding a spot kick Havertz easily converted.
It was one-way traffic again after the break and Germany added a fourth through substitute Fuellkrug's fiercely struck shot in the 69th as Scotland coach Steve Clarke, the first man to lead the team to back-to-back Euros, looked on helplessly.
"First half, we just got it all wrong really, didn't show up, weren't aggressive enough, and we let good players get on the ball," said Scotland captain Andy Robertson.
"Second half, we're down to 10 men and I thought the lads dug in really well. We have to bounce back quickly because there was lots wrong here and it’s a quick turnaround now."
Scotland, who did not have one effort on or off target, pulled a goal back late on when Ruediger inadvertently headed the ball into his own net but substitute Emre Can then curled home a fine shot in stoppage time for the Germans' fifth goal.
The reeling Scots next play the Swiss on Wednesday.