ASP.NET 5 is now ASP.NET Core 1.0
ASP.NET 5 is now ASP.NET Core 1.0
Microsoft eventually decided to go with a new name for their baby. Personally I believe it is a good idea simply due to the fact that it basically should be considered a brand new product.
Read Scott Hanselmans blog on the topic: http://www.hanselman.com/blog/ASPNET5IsDeadIntroducingASPNETCore10AndNETCore10.aspx
Or this one from MSDN:
https://blogs.msdn.microsoft.com/webdev/2016/02/01/an-update-on-asp-net-core-and-net-core/