When you talking about MVC 5 i take it you are talking about ASP.net MVC.
Partial views are used for templates inside your asp framework. All the processing and rendering get done on the server side.
Angular does all of its rendering inside the browser.
Now You can use angular in the page. There is nothing stopping you from using angular on every page you return from your browser.
You don't have to use the router. in the new releases the UI-Router is a separate js file because it is up to the developer to decide what to import.