Tutanota accepts Tor Browser users creating email accounts with their service for free as in gratis: see this blog article for further details.
I have a shortlist of webmail providers that do not have secondary requirements and are free as in gratis, but they may or may not be hosted in the Five Eyes; I do not consider it in my threat model. Other than Tutanota, I have not tested the others for Tor-friendliness.
My specific testing criteria was: English; free tier without third-party invitation requirements and/or a trial period; no advertisements; no email address and/or phone number requirements for signup and/or service usage.
There is also one more webmail provider that is highly likely to meet these requirements, but I have not tested them myself:
Note that unlike your requirements, my focus was on free as in gratis, because I believe secure and private email should be available to everyone first; using them anonymously is an entirely separate issue that is very difficult to practically address.
Other than the Tor Project, I know and am personally involved in a few more related forums to varying degrees: