Is your primary reason to get the room added for resale?
Are you going to just rent it out for now?
If you ever go to sell it your not able to list it as a 5 bedroom unless you permit the room.
Permitting it will entail removing the drywall and possibly insulation so the inspector can make sure the all the utilities (electrical, plumbing, hvac) are installed properly (per code). If they are not, you have to bring all of them up to code.
But, yes it is possible to obtain permitting after the fact.
If you are just renting it out, I am not 100% sure, but I don't think there are any problems with listing the property for rent as you normally would without issues. Rooms that are done without code are usually not the best work done. Hence why they didn't want to pay to get the permit in the first place and usually go with an unlicensed contractor(s) to build it.
You can call your building permit office and ask them specifically about it. They may be able to provide you with specifics answers for this property & even pull up permits that may have been pulled at some point for that room.
EDIT: Most all of the inspectors at the building permit office are aware of the non permitted rooms and are willing to help you do the right thing. It just comes at a cost.
Hope that helps!