Hello,
There appears to be an issue hosting asp.net 5 mvc 6 application when hosting an application as an application inside website.
Below is screenshot contains my hosting environment. I have a ps application inside Admin website. When I browse http://localhost:8084/ps, I get 404 page in the browser.

Then I setup a new website called ps with port 8085 and configured it to point to application wwwroot path, and when I browse the URL http://localhost:8085/ I am able to see the landing page of the application.