School age

My son will be 5 in oct but because the cut off date is sept 30th he won't be able to start kindergarten till next year so he will have to do preschool again. I don't feel like he should have to do preschool again especially if he turns 5 20 days later, knows how to spell his name, count, sing his abcs, is fully potty trained and more! They say they see him as a 3 year old because he didn't turn 4 till after sept 30th of last year!!

Should they go by the child's development on weather or not they can start kindergarten?

Edit we moved from ca to nevada he was in preschool since he was 3!

Edit again

Thank you everyone for your advice i really appreciate it and i do feel better about him staying in preschool another year!