I got my federal refund early but still nothing from the state. Isn’t it also supposed to arrive early since I paid for that?

[xmasbaby0]

No.   "Five days early" was only for your federal refund.

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.  Some states process returns quickly and some are very slow.

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

To track your state refund:    

ttps://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_US_en_US?uid=lt447ebr

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-rev...

[MonikaK1]

If you paid for Early Tax Refund:

Your federal tax refund will be deposited to your selected bank account 5 days before the refund settlement date provided by the IRS (the date your refund would have arrived if sent from the IRS directly). 

TurboTax’s "up to 5 days early" refund option applies only to the federal refund. It works by anticipating information from the IRS, which is separate from state tax authorities. State refunds are processed independently by state agencies, and their timing varies regardless of the early federal option.

Check with your state tax agency as to the status of your state refund. Some states also have a "where's my refund" webpage. See this link for contact information for all state agencies.