I received an application for the alleged 5 points/$ card.

The application is deceptive at first glance, but if you read it carefully, it is clear that it is 3 points/$ at Marriott, and an additional 2 points/$ because of your "elevation" to Silver Elite.

Plain and simple: I have yet to see documentation for any card that offers 5 points /$ in addition to points earned for staying at the hotel.