Denmark to Germany and day trip recommendations from Copenhagen

Where in Germany did you want to go? With only five nights, you'd be pressed to squeeze in a side trip to Germany.

From Copenhagen, some daytrips include Helsingor ("Hamlet's castle"), Hillerød (with Frederiksborg Castle), the Louisiana Museum (modern art in a lovely setting by the water), and Roskilde. Rick's Scandinavia or Snapshot Copenhagen And The Best Of Denmark have details on these places, so you can see which ones interest you.

When in Helsingør/Elsinore consider a visit to the new maritime museum: http://mfs.dk/en/

The German border and Copenhagen are not close to each other (not to mention actual destinations in Germany). You would need to provide far more information about what you were thinking of doing.

I would add to the other great daytrip suggestions that Rosklide is home to the Viking Ship Museum, an excellent display of archeological remains of several types of Viking ships as well as recreated ships. It also has a great cathedral with ornate tombs of Danish royalty.

From Copenhagen to Hamburg, Germany, for instance, takes 5 hours each way by direct train (train goes onto a ferry).

Second the recommendation to visit Roskilde. It is about one hour from Copenhagen by local transportation. The Viking Museum was great and we also visited the cathedral as well.