Can I deduct the California State Taxes paid as an expense or cost on the sale of my rental property?

No, estimated state income taxes are not deductible against your rental gain. However you may be able to deduct it as an Itemized Deduction on your Federal Form 1040, Schedule A, if you itemize. 

• See the TurboTax FAQ: Can I deduct state or local income tax on my federal return?

To enter state estimated income taxes, type estimates paid in the search box and click on the Jump to link.

Your state tax payments are automatically transferred to your state return. We’ll also use them to determine whether you’d benefit from itemized deductions instead of a standard deduction.

You can also use the following step by step instructions.

1. Log onto TurboTax.
2. Select on the blue Pick up where I left off button.
3. On the left navigation bar, click on Federal.
4. Click on the Deductions & Credits tab.
5. At Did you make any estimated tax payments?, select Yes, I did.
6. Continue with the onscreen interview until you get to the Your tax breaks screen. 
7. Scroll down to Estimated Tax Payments and select Start/Add/Edit.
8. At Estimated Tax Payments, click Start.
9. Scroll down to State estimated taxes for 2019 and start.
10. Continue with the onscreen interview. Enter the $5,000 and the date you paid it.