I would like to enable a feature where, 5 days after an order is paid for, the customer is automatically sent a follow up email based on their purchase

What a great idea. This should be implemented. All sellers should focus on providing such outstanding customer service *even if it is automated, lol*
I second this request, shouldn't take much of anyone's time to implement.

Would also like this as well. Would want to have the days setting adjustable, and possibility of sending multiple "drip" email reminders.

+1 excellent idea
 
I was just thinking about this the other day.

Great idea!
 
It would be awesome if you could have different time frames based on product. For instance, we have custom items that ship in 2-4 weeks so the standard 5-10 day follow up (for our standard items) won't work for those.
 
(Just my $.02)