We have 5 minute to get our luggage off a train on platform 5 over to a train on platform 4 in Cologne. I know, it sounds "silly" but are the two platforms next to one another or is there some walking/stairs involved? Five minutes is pretty tight even if the trains are next to one another (unless we're standing at the door when the first train comes to a stop).
Yes, it is a cross platform connection. Its a 20 foot walk.
http://www.bahnhof.de/file/6505234/data/Köln%20Hbf_de_PDF.pdf
Edit-Yes, be standing by the door when the train stops.
Platforms 4 and 5 are opposite sides of the same platform. A plan of the station (Köln Hauptbahnhof) is here.
If the reservation system makes this reservation, it is possible. It is quite normal for German trains to stop on opposite of the same platform to let passengers transfer, and then pull out together on parallel tracks.
It is normal to get up, collect your luggage and go to the train door before it stops. An announcement is normally made ("In a few moments we will be arriving at Köln Hauptbahnhof"). As soon as the train stops people get off, the waiting people get on and the train goes off. The actual stop can be 2 minutes or less. If no more people are getting on or off the train can start. If you are still inside the carriage collecting your belongings, you are liable to be carried on to the next station.
A train is not an airplane. You don't have to remain seated until the train comes to a complete stop in the station.
If you are at the door ready to get off, 5 minutes is plenty of time to walk across the platform.