Thank you! Glad to hear that my posts are appreciated! I like Nigel's idea about a hot air balloon! That will certainly be a memorable trip with amazing views!
A bit cheaper would be to travel by train and make a couple of stops along the way. With five days you have plenty of time to make a few stops. My suggestion would be a stop in Hamburg or Lübeck first, northern Germany is charming and underrated among Americans who seem to prefer southern Germany. Then somewhere a bit more south in Germany, maybe the Rhine valley or some charming town, e.g. Freiburg. Or cross the Rhine to Strasbourg. After that I'd suggest a night or two somewhere in the Alps.
As for day trips to Sweden from Copenhagen, it depends on what you are interested in. But for towns to visit my suggestion is Helsingborg, Lund or Ystad.