Here is a relevant excerpt from the New York State Education Department (NYSED)'s website that answers your question for that state:
"Children must reach their...5th birthday by December 1 or the date established by the public school district for entrance to kindergarten in which the child resides."
Here is a relevant excerpt from the Florida Department of Education website that answers your question for that state:
"Florida law (Section 1003.21(1)(a)2, Florida Statutes) specifies that children who have attained the age of five years on or before September 1 of the school year are eligible for admission to public kindergarten during that school year based on rules prescribed by the school board. Students are eligible for kindergarten attendance provided they meet the age requirement."
You can locate the contact information for the local school districts in both states via SchoolFinder (enter your city, state and zip code for a listing of local schools and the district).
I'm also including a link below to some additional resources to prepare you and your child for the year ahead. Congrats on this special milestone for your family, and especially for your young student!