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====Bottom Line====*You'll notice that if If you spend over $5,950/year you are actually making more money with the 5% card AND you have a Prime membership. So if you spend that much, it is a no brainer. You should pay for the Prime account and use a 5% card.
*If you spend less than $5,950/year and you kinda like the Prime membership benefits, then you have to decide if the "discounted" Prime membership is worth it.
*If you don't value the Prime membership benefits and you spend less than $5,950/year then you should just go with the 3% card and skip the Prime membership.