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Regardless of whether Venmo would work, the offer itself isn’t that great. I’d wait until another 100k Platinum offer comes around and it usually has a smaller spend requirement than $5k
I would not even try it, using Venmo, Paypal (send only), Square Cash, or the likes will get you a FR and your accounts frozen faster than you can say Amex. They do not like their cards being used for P2P payments.
I can personally vouch for the fact that purchases through Square or PayPal are hit or miss when it comes to being credited for rewards or minimum spend. I wouldn't risk it.
Godspeed with that one.
Paypal/Venmo are very shaky for AMEX. I would never ever ever send money to someone via paypal with my AMEX, especially if I live with them.
AMEX may flag you, freeze your accounts, and possibly cancel them.