Update (2022): It may be possible to earn double the amounts listed in this answercash back for new accounts that receive double cash back in the first year. I cannot find anything in the terms or conditions that would exclude this. If that's the case and you maxed out the offer, then you could add an additional $75 to your profit listed below.
Congrats! You found a legitimate arbitrage situation that indeed could make you some money. These are increasingly rare, which does make it kind of cool, even if you end up not taking advantage of it. IMHO it's not worth it due to the spending cap.
The deal you Discovered appears to pay 5% on PayPal transactions, including those made to friends and family, but unfortunately it is capped at $1500. So, the maximum cash back you can achieve is $75. The minimum the PayPal fees would be is 2.9% + $0.30 for a single transaction, which is $43.80. Your profit from this would be $31.20 minus whatever you have to give to your friend to convince them to go along with it and give you your money back.
In the US, cash back on purchases from individuals (but not businesses) is typically treated as a discount on your purchase, and is not taxable.