If it is through auto renewal via that credit card, then it should attract 5% cb to my understanding as there was no stopgap on your membership in between and it was continued from the existing one.
If your membership has already been expired and you are buying it manually through that cc, you won't get 5% as you were not a prime member at the time of buying the membership.
Not related to your question but I bought Amazon Prime (1 year) using Millennia CC, and got 5% cb. So, basically Millennia considered it as a product purchase. Not sure about Amazon Pay CC.