Well, if you have 3 months to spend $5,000, that's under $1,700/month. Just try to put everything you buy on the Amex for a few months (gas, restaurants, travel, entertainment, coffee, etc.). For companies that don't take Amex, go elsewhere or try Plastiq. If this is a one-off card, there's no real need to resort to manufactured spending...just use the card for stuff you buy.