This was Bayern’s worst game of the season so far, as well as the worst in many years.
"I'm absolutely shocked. We simply didn't turn up," Bayern sports director Hasan Salihamidzic told ARD.
"We let ourselves be outplayed in every situation - a collective blackout."
Full-strength Bayern conceded the first goal after just 71 seconds and were 3-0 down with 21 minutes played as Gladbach made a lightning start.
It was the first time in 27 years Bayern have conceded so many goals so early in any competition.
Bayern crashed to their heaviest German Cup defeat, eclipsing a 5-1 quarter-final defeat at Cologne in 1972.
"From time to time, you dream of something like this, but you don't believe it will become reality," Gladbach sports director Max Eberl told ARD.
"That was an awesome performance."
French midfielder Kouadio Kone grabbed his first goal for Gladbach with barely a minute gone, then Algerian defender Ramy Bensebaini and Swiss striker Breel Embolo both scored twice.
"5-0 against Bayern doesn't come along very often, so we will enjoy this tonight," said Embolo.
This is the second time in consecutive seasons Bayern have been dumped out of the cup in the second round having lost at Holstein Kiel last January after a penalty shoot-out.
Also, Bensebaini has terrorized Bayern for the 2nd time after the 26-year-old scored both goals in Gladbach's 2-1 home Bundesliga in December 2019. Embolo then compounded Bayern's misery with two rapid-fire goals within six minutes of each other to make it 5-0 after 57 minutes.
The celebrations of home team fans started with ten minutes left as delighted home fans sang 'Oh, wie ist das schoen' (Oh, how beautiful this is).