Think about it like this, it's not smoke going back it, it's airflow dynamics. You have a 5" hole and "maybe" the outside air difference is coming in and helping cause the issue.
There are a lot of solutions.
Me? I kept it simple. I just went out and bought a cap, cut it down so it slips right over the hole. I'll have to take a photo, but with 60mph winds in Oklahoma (wind chill -20) I need it somedays.