It depends on whether you are traveling by car or some other means of transportation, where you're coming from and where you're heading, but I did a drive last year from Plitvice Lakes (in Croatia) through Bosnia, and then to Split (back in Croatia again). That will take you through some interesting places from a local culture and history perspective:
Bihać (I stopped for a few hours)
Jajce (I stopped for a few hours)
Sarajevo (I spent three nights)
Mostar (I spent one night)
Počitelj (I stopped for a few hours)
You could detour off my route to other places, but I can only speak to the places I visited. You will also see some wonderful scenery on this route.
Sarajevo is worth the majority of your time if you have 4-5 days. It is in a lovely setting in a valley surrounded my mountains, and there are not a ton of tourists, so you will really have the opportunity to immerse yourself in local culture.