In this case, wouldn’t she still be a dependent (assuming she graduated in May and started the job in July). If she was a student, did she earn enough to support herself for the first 5 months? I believe scholarships/grants/loans are not counted as providing support.
In my case, my daughter started her job at the end of June. We pay for the first month rent (Juy) since she was not paid until end of July. As far as I can tell she is our tax dependent for this year.