Midfield pair Cameron Howieson and Jaden Hill and striker Jason Gilchrist - all first-year professionals - along with second-year pros defender Tom Anderson and midfielder Steven Hewitt have been given terms to remain with the Clarets.
However, former Blackburn winger Micah Evans is among those who are free to find a new club. Jack Errington, Kyle Brownhill, Luke Conlan, Luke Gallagher, Alex Coleman and Archie Love will also not be offered fresh contracts by boss Sean Dyche.
"This is a tough time of year as a manager because, along with the really good stories about the young professionals we are keeping as part of the future of the club, we also have to let young people know that we are not retaining their services," said Dyche.
"We wish those players well for their future and we have assured all of them that, as part of our beliefs, we will try to enable them to continue their careers in football.
"We do have a responsibility to look after these players as best we can and align them with their next pathway."