The tests are different for the county, state and city

I think the best way is call and ask them.

Usually for the State of California Jobs, you need to take the test first, then you will be on the eligible list. Only
rank 1-3 can apply for the openings. But the ranks will move-up(though you have rank 5 now, you may be rank 2 or 3 in the future).

County have similar procedures. Basically, for the written test, it will ask your experience about how to handle different scenarios(like, as Accountant, when you found an error, what are you going to do? If you have the access the individual's private info, can you leave the printout at the computer, etc.

The best way is to call and ask them. I know some agency will give you 4 to 6 questions ahead of time.