If your parents can only contribute $5000/year and you as a student can only take out $5500 as a Freshman, that will be the extent of your budget unless you qualify for Federal aid (Pell Grants). Are you parents willing to take out a Parent plus loan on top of the $5000/year? What is your family EFC?
What you need to do is figure out what your budget is first and then look for schools that will give you good financial aid and/or merit aid.
The Cal States (CSU’s) run about $40,000/year for an OOS applicant and offer little to no financial aid or merit aid.
You would need to target private schools not public schools that offer good FA.
I would look at University of San Diego, Occidental, St. Mary’s, Azusa Pacific and University of San Francisco as possible options but not sure if these schools will fit your requirements based on intended major. Run the net price calculators on each of the schools to get an idea of costs.
Without the help of your parents, I seriously doubt you will be able to afford any California schools but do some research.