For what it’s worth, that doesn’t sound typical to me. I’d say pre-school, it’s it’s done at all, is done at the age of 4 - maybe 3 if you’re doing it super early. I’ve never heard of “K4” and “K5,” and most kids start kindergarten at age 5 and only do one year of it.
Where is "here"? In the upper midwest, "Pre-K"/"4K" is age four. Kindergarten is age 5. There is not typically anything earlier than that, and parents are on the hook to find their own daycare if not home with the child.
Where do you live?