.net core cookies authentication on browser close

I am using cookies authentication in my .net core mvc application. One of the requirements I have is to logout user when the browser is closed. I have set sliding expiration to 5 minutes in app. As expected if the user comes back to the website after 5 minutes user is redirected to login page, but if the user comes back inside 5 minutes the user is logged in automatically. Is there a way to logout user if the browser is closed?