Answer:   .NET 5: It is the next generation of ASP.NET that provides a familiar and modern framework for web and cloud scenarios. It includes the next versions of ASP.NET MVC, Web API, Web Pages and SignalR. It is a high-performance and modular design and supports full side by side to make it seamless to migrate from on premise to the cloud. These products are actively developed by the ASP.NET team in collaboration with a community of open source developers. Together we are dedicated to creating the best possible platform for web development.
.NET Core: .NET Core is the small optimized runtime that is the basis of ASP.NET Core. It currently runs on Windows, Linux, and Mac. It is a high-performance and modular design, and supports having several applications on a web server each one with its own copy of the .NET Core runtime, enabling a full side by side experience, and that will make it easy to adopt new .NET Core versions without affecting other apps, and this makes .NET Core architecture a leap forward from the current classic .NET 4.6. These products are actively developed by the .NET team and in collaboration with a community of open source developers. Together we are dedicated to improving and extending the .NET platform with new features and for new scenarios.
.NET Core has two major components. It includes a small runtime that is built from the same codebase as the .NET Framework CLR. The .NET Core runtime includes the same GC and JIT but doesn’t include features like Application Domains or Code Access Security. The runtime is delivered on NuGet, via the Microsoft.CoreCLR package.
.NET Core also includes the base class libraries. These libraries are largely the same code as the .NET Framework class libraries but have been factored (removal of dependencies) to enable us to ship a smaller set of libraries.