NET 5 doesn't exist yet. It is .NET 4.6 which was just released. The latest version of ASP.NET is version 5.0, which uses up to .NET 4.6. .NET Core 5 is a totally different thing, and there aren't predefined migration paths to it.
You can't just convert a regular ASP.NET 4 project to a ASP.NET 5 project since the introduction of the entirely new Core framework. You have to do it by hand yourself.