If you had 5 days in Sweden, which would you visit and why?
It would depend on which city I was landing in first.
They are both attractive, but Stockholm is easily more-to-see-and-do. You have failed to say if you have ever been in Sweden before. That would make a big difference in our answers. It would also help if you filled in your home state and city, so we knew if you live next to L.A. or somewhere in the woods.
I would put the local symphony orchestra, and Liseberg Park (an unusual amusement park, by American standards) at the head of Gothenburg's attractions, as well as being closer to Denmark. What's unusual about Liseberg is the laid-back, extreme-Knott's Berry Farm ambiance, as opposed to the Disney/Universal frantic pace and desperate families rushing about in the U.S. Stockholm is worth repeated visits.
If you've never been to either then I would say Stockholm - Stockholm can easily fill 5 days, not so sure about Gothenburg. Of course, just for logistics, it may depend on where you are coming from and where you are going after. It's not a long train ride between them (<4 hrs) so you could spend 3 days in Stockholm and 2 in Gothenburg. It also may depend on if you'll have a car at your disposal and where you may want to go on a day trip from either one. So, lots of ifs.
Our home state is Arizona. Although we've traveled throughout Europe and Mexico, we have not yet visitied Scandanavia. We are a senior couple and will be visiting Norway first, then on to Sweden and will finish our trip in Denmark. We are trying to decide between the longer trip to Stockholm, or spending time in Gothenburg.