Goalkeeper Nick Townsend, defenders James Fry and Ryan Higgins, midfielder Charlee Adams and striker Reece Hales, all aged 18, have been handed the deals with a further one-year option.
Midfielder Jean Kalenda has also been offered a third-year scholarship.
Lee Clark and Academy Manager Kristjaan Speakman informed the crop of trainees earlier this week.
Commenting on the offers on the eve of Academy Day at St. Andrew's, Clark told bcfc.com: "I’ve said to them that they’ve got a contract and why not from the end of June when we come back for pre-season are they not pushing for a place in the first team because everyone has seen how I’ve talked the talk but also walked the walk in terms of the young players.
"I’ve said I’ll give them an opportunity and I have. It’s down to them now. I put a 17-year-old (Koby Arthur) on in a massive midlands derby on Monday ahead of some more senior players."
Speakman added: “It’s a fantastic achievement for the lads and a difficult stage for them personally with the ambiguity surrounding their registrations. It is however a factor of the environment we operate in.
"We are delighted that five of them have gained further terms with the club from the scholarship programme.”