It's different for every district.
In Milwaukee, students who turn 5 in September enroll in K4, then can get tested and promoted early in the school year.
My SD with a similar birthday, in Madison, got tested during the summer. She had to retest but was allowed in (which is a *good* thing--she's reading at a 3rd-grade level and would have been bored off her rocker with an extra year of preschool, and just starting K5 now).
ProtoLawyer (the now-actual lawyer, this isn't legal advice, please don't take legal advice from some anonymous yahoo on the Internet)
Spouse (the political geek) * Stepdaughter (the artist) * and introducing...the Baby (um, he's a baby? He likes shiny things).