I happened to hover over the Prime tab on my Amazon US home page this morning, and found an offer for a $5 credit if I buy $50 worth of e-gift cards. It's billed as a "Mothers Day" offer, but I don't see any specific time frame actually mentioned.
I have sent myself a $50 e-gift card, and will come back and update if I have any issues getting the $5 credit.
The link was:
https://www.amazon.com/b?node=102952850011
And since it says at the top "Congrats, you're eligible for this offer", I suspect it may be a generic link. Maybe someone else can come back here and post if it worked for them.
Or else you can try hovering over your own "Prime" tab...
And, of course, as I always do with such offers, I have a screenshot of the offer in case I have to go argue for it

!