Bruntsfield, Liberton, Newcraighall, St Margaret’s RC and Trinity primaries have all been included in the latest phase of the city’s rising rolls programme.
And it has emerged Stockbridge and Victoria primaries – where space-boosting work has already been carried out – have been lined up for fresh investment as teachers prepare for surging demand beyond 2017.
Education bosses said each school was operating under unique circumstances and that the options available to address accommodation issues would vary.
Estimates also show the overall bill for campus expansions and revamps in Edinburgh is likely to jump to £21.58m by 2020-21.
With just under £20m set aside, city leaders have admitted they will need to find nearly £1.7m to plug the gap.
Opposition figures said the problem of crowded schools would only be solved through proper planning.
Councillor Melanie Main, education spokeswoman for the Greens, said: “When extensions built in playgrounds within the last couple of years are not enough to cope with the continuing rise in rolls and more building is required, continuing this piecemeal approach has to be seriously questioned.
“I have always argued for a long-term approach to the schools estate and, with the rising rolls moving into secondary schools, this is needed now more than ever.”
Updated projections show the city-wide primary roll will increase from 28,804 pupils at the start of the 2015-16 session to an estimated 31,300 by 2020, and then increase further to 35,400 by 2030.
Parent leaders said the council appeared to have the school space issue under control.
Alex Ramage, parent representative on the city’s education committee, said: “What the council has chosen to do is look at it each year, at the start of the session, when we know which schools will be in a difficult situation, and say, ‘we will extend those schools if necessary’.
“That seems an entirely sensible approach.”
City bosses stressed that the budget for expanding overcrowded schools had already been quadrupled to nearly £20m.
Education leader Councillor Paul Godzik said: “Over the past three years we have delivered an additional 70 modern, high-quality class spaces in our primary school estate, which have been very much welcomed by staff, parents and pupils.
“However it is clear that, given the continued rise in pupil numbers and the expected pressure on the secondary estate, additional resources in future capital budgets will need to be identified.”