Johanso,
I would be very interested in some info about where a few must see place would be if I had 4-5 days in September next year. Im planning a return from Iceland at the end of August and then moving north for a week or two.
September is a great time of the year to explore the Nordics. Days are still pretty long and warm, not much mosquitos left so great time for spending time in the mountains and forests.
The distances are big in this region so it depends a bit on where your start from. If you start in southern Sweden for instance you won't have time to drive to the most northern region with just 4-5 days at hand. Well, if you spend all the time in the car it would work but that won't be much fun.
The coast of Norway is spectacular and more or less a must see. Just a couple of hours inland you can visit mountains for great hiking and other fun stuff.
I you have time, Sarek and Abisko national parks in Northern Sweden is really beautiful with untouched wilderness. From there you can drive over to Norway and see the coast. September might be too late to go on whale safari but otherwise that is a great experience.
Let me know where you are starting from and I can give you some more ideas.