I filed an amended paper return on May 3 for state and federal. Both sites are telling me that they have not been processed yet. Any new info on processing dates?

The Federal Amended Tax Return, Form 1040X, had to be printed, signed, dated and mailed by you to the IRS.

The State amended tax return had to be mailed to your state.

For the status of a federal amended tax return use this IRS website - https://www.irs.gov/filing/wheres-my-amended-return

The IRS was not processing any paper tax returns for several months due to the pandemic and limited staffing.  They have only just recently started to process approximately 11 million paper tax returns in the order received.

Go to this IRS website for information - https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue

We’re experiencing delays in processing paper tax returns due to limited staffing. If you already filed a paper return, we will process it in the order we received it.

Do not file a second tax return or contact the IRS about the status of your return.

For the status of the State amended tax return you would need to contact your state tax department of revenue for the status.  See this TurboTax support FAQ for state department of revenue contacts - https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/01/25573