Why have I not received my state refund yet? I filed and it was excepted five months ago

Once a tax return has been Accepted by the IRS or a State, TurboTax receives no further information concerning the tax return or the status of any tax refund.  

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...

Also....print out a copy of your State tax return, to make sure a "refund" is indicated on the appropriate line for your state forms.  (Also #2: make sure you didn't indicate you let the state keep the refund as a prepayment for next year's taxes....that would also be shown on the state form)