With an Amazon card at 5% on Amazon purchases (up to $120k) all you need to spend is < $4000/year and it breaks even. There are reasons that make sense to stop using prime, but not for the money, it’s still a steal.
I dont think you are quite right. To the best of my knowledge, you get 3% back on the Amazon branded cards. If you have prime, then you get 2 more percentage to a total of 5%. So to make up for the difference of $139, the price of prime in terms of cash back, you have to spend $6950 (or ~7000 as the OP said) to break even.
Now if you have Discover or Chase Freedom, they run the 5% quarterly bonus (for the first $1500 spent on the bonus category) at least once a year, so your break even point is even more than what I mentioned earlier (closer to $10K).
