American Express is not interested in individual circumstances. Five is the maximum number of credit cards, it's not a suggested number or a typical number.
Business and Personal both count. Blue Business Plus is unambiguously a credit card. You just need to use the cards that you have until you can safely close one.
I stand by what I have said earlier. I just logged into my AMEX account and recount all of my active cards. If I include the BBP, I have 6 credit cards (business and personal).