Laws for cut-off dates for kindergarten admission are determined by each state. In California, your child must be 5 years of age on or before December 2 of the school year, according to the California Dept. of Education, so it looks like you just missed the date. Schools are generally pretty strict about the cut-off date, but it's always a good idea to check directly with the school or district you are interested in.
The rules for school boundaries and admission vary by district. Some districts have "open" enrollment, where you can attend any school in the district, so long as there is room, while others assign students by neighborhood. Some districts may allow "intradistrist" transfers from one assigned school to another school within the district or "interdistrict" transfers, from a school in one district to a school in a different district. Generally these transfer arrangements only apply if there is space available at the school you want your child to attend. California also has a law called the Allen Bill, which allows you to transfer your child to a school in another district if you are employed in that district or have a childcare arrangement before or after school in that district.

Some school districts have magnet and/or charter schools that are open to any student in the district. These schools generally have a specific philosophy or thematic curriculum, such as an arts or technology academy.

In any case, as healthy11 says, it's always a good idea to check directly with the school or school district to find out what regulations apply.
For general information about choosing the right school for your child, check our School Choice Tips page:
www.greatschools.net/content/schoolChoiceCenter.page