Mrs. Tdyls and I will be traveling to Amsterdam this November on SAS, and we have a connection in CPH for a little over 5 hours. To me, 5 hours is right in the Bermuda Triangle of "too long of a connection" to stay in the airport, and "too short of a connection" to really get out and explore. However, given that you will be able to measure the amount of sleep we get on the redeye across the Atlantic in minutes, if not seconds, one thing I'm considering if it's a nice day is to do a 2- or 3-hour whirlwind tour of Copenhagen during our layover to fight off the sleep deprivation and jet lag. My question is if that's worth the hassle. I know it CAN be done, but SHOULD it? Our tickets are premium economy so we will have access to the SAS lounge, and the idea of taking a shower, and getting hot coffee and breakfast is a pretty compelling reason to stay in the terminal. (Obviously if the weather is raw, rainy, yucky, then the decision is made, but if it's reasonably sunny out or if there's a great tailwind and we get into CPH an hour early...)

The way I see it, the itinerary would be something like this:
10:00 AM: land in CPH
10-11: Clear EU customs, check carry-on luggage at a luggage storage place, walk to Copenhagen subway, and take the subway to Kongens Nytorv
11-1:15: Walk 3.25-mile loop and see Kongens Nytorv plaza, Nyhavn, Little Mermaid, Kastellet, and Marmorkirke. Have a quick lunch en route.
1:15-2:00 Take subway back from Kongens Nytorv to the Airport, reclaim luggage, go through security
2:30 Get to gate for 3:30 flight to AMS

It leaves some margin of error, and Copenhagen tourist websites do promote variations of the 5-hour tour, so I know it CAN be done. But is the return on investment there? I know that this is barely even scratching the surface of Copenhagen, but do you think it'd be a nice teaser/introduction to justify all of the extra hassle/schlepping?

You don't need to decide anything ahead of time. Wait to see how you feel, how long it takes for immigration, and IF you land anywhere near on time. If all is like clock work - then sure. Are you flying Business or do you have status -- if you are beat or you have less time than expected you can use the lounges. And if you don't qualify, there are for-pay lounges.

(You won't have any 'Customs' - that is for luggage and any declarations -- assuming this is all on one booking you will do Customs at AMS. You will go through Immigration i.e. Passport Control at CPH)

Postscript to this, written in August 2025:

We ended up staying in the SAS lounge en-route to AMS.

But we're unexpectedly going to be able to see Copenhagen anyway, because we were able to get unexpected cheap tickets roundtrip to CPH for February 2026. It'll be cold, dark, gray, and definitely off-season, but my wife wanted to practice Hygge this winter, so why not do it in Hygge-land!