An event is only shown if it is in the current month. It it is set to show 5 events it should show the next 5 events regardless of the month. Customers need to see the next 30 days not the current month especially toward the end of the month. Can the widget list more than 1 months events?
Currently, the plugin is designed to show the current calendar month regardless of what day of the month it is. One possible alternative is to use the Upcoming Events widget instead of the Events Calendar widget. Or you could possibly make this customization if it suits your needs: https://theeventscalendar.com/remove-calendar-image-from-calendar-widget/. I don’t think either of those is exactly what you are looking for though. If you’d like to add this idea to our Feature Ideas page (https://tribe.uservoice.com/forums/195723-feature-ideas) that would help us in prioritizing it.
Sorry we don’t have a perfect solution for you at the present time.