Hi @iqworks Information Quality Works ,
First, the .net 5.0 razor class library is based on the .NET but the Asp.net 4.7 MVC is based on the .NET Framework, you can't add the .net 5.0 razor class library to the 4.7 MVC project. About the difference between them, see Compare ASP.NET Core and ASP.NET.
Second, the .net 5.0 razor class library is a class library, when using it, you need to add the class library to an Asp.net (5/6) Razor page or MVC application, then in the 4.7 MVC project, you can call the Asp.net 5 (I assume you will create an Asp.net 5 Razor page application and add the class library) project's razor page/view via the http request and get the response.
Here are some relates articles about using Razor class library:
Create reusable UI using the Razor class library project in ASP.NET Core
Working with Razor Class Libraries in ASP.NET Core
Then, in the 4.7 MVC application, you can use JQuery ajax or HttpClient to call the Asp.net 5 project's page/views.
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Best regards,
Dillion