Children as young as five are being rejected by NSW public schools because their parents are temporary visa holders while schools across Sydney overflow with enrolments.

Five-year-old Frederico Jemma was born in Sydney to Italian parents who have lived in NSW for seven years on temporary visas. Both have paid taxes and are happy to stump up the $5000 it costs to send an international student to a local public school.

But in September they were told there was no room for Frederico at Kensington Public.

Enrolments have skyrocketed by between three and five times the NSW average over the past four years across the Waverley, Canada Bay, Sydney and Ryde local government areas, according to a Fairfax Media analysis of Department of Education figures. At Kensington Public they have surged 14 per cent in that time alone.