Remote Backups Filling Up Disk

Hi there, I am at the heart a coder, but have recently begun hosting websites (mostly simulation games). At this time I have a setup where my main server retains 5 days of backups and my remote server receives the backups each night. I recently got a notification that the secondary server was almost full, meaning that copies of backups aren't being deleted as far as I can tell. What is the next step here? Thank you.