My Federal Refund was accepted on 01/23/2024 but my CA State return still hasn't been accepted after 5 days. Is this normal or should I worry?

It's not necessarily uncommon.  Your federal return must always be accepted before your state return is submitted for acceptance.

That said, if you're concerned about the status of your state return, see the TurboTax Help article How do I track my state refund? for tracking guidance.

Thank You John,

After reviewing the forum I realized I wasn't the only one.  I did file my taxes much earlier than I normally do, so I was a bit uneasy.   I'm going to wait until after Jan.29th and see what happens... I'm sure things will be fine.

IRS accepted a test batch of returns yours was clearly one of them as you mention season starts on the 29th and it could take up to 48 hours after that