why would you want to dump the user out when they are in the middle of reading something or filling in a form?
You have said this is exactly what you are trying to avoid!
On every load if a page, or ajax request to a web route, the session timer will be extended.
If you still want to refresh the page use a meta refresh tag. no need to mess about with local storage - but set it in terms of hours not 5 minutes ( which is probably less time than an average phone call)