In a non persistable object associated with your session, you could store if it was already showing up or not. Then you can access your home page via a microflow. This microflow checks the non persistable object if the popup was already showing before (if not existing it would create this object). If it was not already showing, the microflow not only opens your homepage, but also a popup page.
On this popup page you can now use the microflow timer widget from the appstore and configure it in a way that it executes a microflow after 5 seconds, that is only closing the page.