I had a 2025 federal tax return rejected and now turbo tax is saying I hit my 5 filing limit. Does the rejected return count as part of the 5 and if not, how do I fix?

You will need to paper file. 

The IRS permits 5 e-files; it does not appear to differentiate between accepted and rejected e-file returns. 

That is an IRS limitation, not a Turbo Tax limitation.