What kind of application are we talking about? Desktop? Web Applications?
CoreFX is just a modular version of the .NET Framework modular, but it won't "link" (similar to C++ development) any assemblies to the main executable.
CoreFX will allow multiple side-by-side applications, so when you update one application to new modules other CoreFX applications won't be affected by it.
But (at least for now) CoreFX is a targeted for cloud and server applications so far and do not have the full feature of the .NET 4.6 framework, nor does it have or support GUI framework (WPF, WinForms).
So if you're aiming for Web-applications, you can use it soon (it's not released yet. As of the time of writing, it will be released in 3 weeks on 20th July 2015). If you want Mobile or Desktop Applications you have to stick to the full .NET 4.6/4.5 Framework and then your app will require the appropriate .NET Framework to be installed on your PC before the application can be used.
i.e. you won't be able to use EntityFramework 6.x with CoreFx, as it depends on the full .NET framework implementation and EF 7.x do not support all Db providers yet and do not have all features of 6.x neither.
This won't change anytime soon. And if you use it, be aware of the limitations.
Check out this issue of corefx issue tracker addressing your exact question:
https://github.com/dotnet/corefx/issues/165
Will you be able to create desktop programs in VS2015 that targets
.NETCore 5 or .NETFramework 4.6 (they are separate correct?). Right
now in VS2013 it seems you can only target .NETCore when creating
windows store apps. I cannot seem to target .NETCore when creating
desktop applications.
.NET Core is currently focused on server-side scenarios, no GUI technologies like WinForms/WPF etc. .NET Framework 4.6 on the other hand contains everything, so you can create Desktop apps with it.
Will .NETCore 5 need a runtime installation for .NETCore programs to
work on the target computer (whether it would be windows, mac or
linux), or will I be able to include the runtime as part of the
program?
.NET Core can be deployed alongside your application, so it doesn't need a runtime installed.
Which brings me to another question, if a installation is required for
.NETCore runtime, will the .net Framework 4.6 installer install
.NETCore 5 with it (limited to Windows only)?
See 2.