Yes, you are right, if you are on 5.0+, however the 4.x stuff is definitely out of support.
Sorry, I did not know they had actually brought non-Core ASP.NET forward into 5.0+, but it makes sense given how much of .NET Framework they continued support for and how much ASP.NET and Forms stuff is still around in enterprise with no budget for bringing it forward.
Totally agree with breaking the chain though, we moved to Core around 2.0 and never looked back, as an ecosystem it is so much better.
> however the 4.x stuff is definitely out of support [...] Sorry, I did not know they had actually brought non-Core ASP.NET forward into 5.0+
None of this is true, you've gotten yourself very confused. The only real change with .NET 5 was the "Core" name being dropped and the Mono runtime being merged in. .NET Framework 4.x is still around and is still fully supported for legacy applications.
This is, IMO, a bad thing, and Microsoft needs to break this chain at some point, at least for ASP.NET. But, it is still technically supported.