While it can be hard to tell what's exactly the issue with VS or local environment you have, it should be possible to temporary create projects with dotnet cli:

dotnet new console --output <project-dir>

If you would want to add it to an existing solution run

dotnet sln <solution-name>.sln add <project-dir>

The console app project file is very simple, so you can even create it manually, or create a project from any existing template and replace the contents with following asa workaround:

<Project Sdk="Microsoft.NET.Sdk">

  <PropertyGroup>
    <OutputType>Exe</OutputType>
    <TargetFramework>net5.0</TargetFramework>
  </PropertyGroup>

</Project>

And maybe one more thing you could try is to run the VS installer as admin or ensure that it can install and access all the required components.

I have VS 2019 version 16.9.5 when I seen your post. I am using console app for my sample projects. I have tried it and able to achieve what you are looking for. I would recommend to update your VS to 16.9.5 and give it a try.

My VS 2019 version:

Creating Console app in VS 2019 16.9.5:

Finally it has created a console app project with target framework as .net 5.0

Eventually clear the MEF component cache, manually or with this extension.

But most likely something is wrong in the user cache at C:\Users\USERNAME\AppData\Local\Microsoft\VisualStudio\16.0_93de0ddd, which includes in particular InstalledTemplates.json and privateregistry.bin.

Try and rename (or delete) the folder, (or one the the two mentionned files to narrow the problem down), while VS is off, and restart VS. Only make sure that you have the proper workloads installed and the .net 5 from VS.

I checked and I am able to create dotnet5.0 console application with visual studio version 16.9.2 and SDK version 5.0.201. I think there is some installation conflict on your end. You can try uninstalling the SDK and reinstalling visual studio or updating it to latest version and downloading latest SDK. Also check if SDK is getting installed on your system under

C:\Program Files\dotnet\sdk[your SDK version]\

I ran into this problem on VS2022 Preview 7.0.

Upon doing dotnet --version I got back 5.0.100-preview.6.20318.15, I must have installed it some time ago and it was still on the system path. So I downloaded and installed dotnet 6.0.100-rc.2.21505.57

After that VS started working as it should.

EDIT: I just got lucky. I'm now on VS2022 17.1.0 Preview 1.1 and am running the production versions of .Net 5.0.403 & .Net 6.0.100.
The problem mysteriously came back. I did not knowingly change anything. My best guess is it broke weeks ago when I upgraded VS2022 and I just haven't realized till now.

I've completely and painstakingly uninstalled EVERYTHING. VisualStudio 2019 & 2022 as well as all of dotnet core and 5.0 & 6.0. I even got all the remnants I didn't know stuck around from years ago. I then reinstalled everything and still, no Net5.0 or Net6.0 templates.

I noticed that the uninstall strings for the .NET Template packages have an /I for install prefix instead of /X for uninstall. I figured maybe this could mean the packages aren't actually installed, so I've tried to run them manually but that fails. I'm out of ideas.

So far the only successful way I've had to create a net5.0 or net6.0 project in visual studio is by downloading Classic Console Template, which provides enough bootstrapping to actually create a new project.