How to set up 'renewal reminders' 5 days after renewal, and filter by a group
I spent some time looking through the source code and the history of this feature.  After review, I think you're best off trying to implement this via CiviRules instead.


Your CiviRules trigger should be "Activity added", not membership-related.  Otherwise you run into similar limitations as the Scheduled Reminders approach.
Your conditions can be "Activity is of type: Membership Renewal" and "Contact is in Group: X".
You'll also need to install the Email API extension so you can add an action of "Send Email".