Heneghan Peng Architects, Niall McLaughlin Architects, O'Donnell + Tuomey Architects, Panter Hudspith Architects and the Consarc Design Group have made it onto the final list.
This group saw off competiton from 54 expressions of interest received from the UK, Ireland, Europe, Australia and the USA.
The scheme will see the construction of a new museum which may or may not include a new library, depending on a current funding bid.
'Selecting only five architect-led design teams from such a strong field was very difficult,' the RIBA advisor on the project Clare Wright said.
'All those chosen demonstrated exceptional design talent, experience of museum display and storage and an aptitude for working in a historical building context.
'They also showed an understanding of the importance of local consultation for a building to display and illuminate the history of the region,' she added.