I recently retired from a broke midwestern state. 5 weeks of vacation is pretty much the norm for exempt from overtime employees. Regular employees start off with 12 days vacation and work their way up. Everybody accrues 12 sick days per year, but that doesn't mean they can use it like vacation. They stopped direct sick leave payouts in the late 90's. A years worth of accrued sick days can be applied to certain retirement scenarios, but not all. New hires can accrue sick days, but that is about all.
Similar in Cal state service. I am retired now. We started with 2 weeks and worked our way up to 4 after 25 years. When we retired, any unused sick leave was credited on the work years side of our retirement formula. I had a years worth of SL and got an extra year credited toward my service.
SL is one of the most abused benefits in Cal state service. However, you can roll it over forever and have some credit at retirement.