The Nutshell route can be completed in one (quite long) day--at least in high season. Some of the transportation links run less frequently in April. I spent two nights in Flam, and some folks have really enjoyed spending multiple nights in Balestrand. But I'm curious about the itinerary for a 5-day tour. I'd expect a tour to have its own transportation to supplement the Flamsbana Railway and the Flam-Gudvangen ferry, so it should be able to move around efficiently. I'd think 5 days would be long enough to cover more than the traditional Nutshell route. The fjords are gorgeous (when the weather cooperates), but that is a lot of time in fjord country all in one block.
Nothing I've read about the express boat to Bergen has made me interested in taking it. The narrow fjords are more scenic than much of that route.
Oslo and Bergen are both very worthwhile. Perhaps 3 days in Bergen would be 1 more than you need since you would already have spent a lot of time around the fjords. The city is very pretty, so it's easy to spend time just wandering around, enjoying the urban scenery (but weather is really, really iffy there). It has multiple worthwhile art museums, though one of the four KODE branches was closed in June). I didn't go to any of the older historic sites except the rebuilt stave church, but Rick's description of them is that they are generally visually underwhelming and more meaningful if you take a tour.
Oslo has a lot more museums, and a wider variety of them. The architecture is more varied. There are new museums like the MUNCH and the National Gallery. There's more to do indoors if you are not lucky with the weather, and Oslo is generally much, much less rainy than Bergen. Take a look at the climate-summary charts in Wikipedia's entries for the two cities.