Normally you can earn 10,000 HHonors bonus points after your first purchase as well as 2,500 HHonors bonus points for each of your first four stays at a Hilton hotel, for a total of 20,000 bonus points.

During the current promotion, you can also earn an additional 15,000 bonus points after you spend $5,000 in five months. It should be noted that this is not the most lucrative offer that Amex has ever offered for the Hilton card, as late last year, 30,000 bonus points were offered for $5,000 in spending. Still, it represents a significant upgrade over the standard offer.

So, here’s the math:

 10,000 point bonus from 4 stays @ 2,500 bonus points each
 30,000 points from spending $5,000 in 5 months (15,000 points for your spending + 15,000 points bonus)
+10,000 point bonus after your first purchase
——————————————————–
50,000 total points under this offer

The application can be found here.

To sweeten the deal, consider waiting until you have the card to add more card holders as Amex periodically offers bonus points for this activity. You can potentially earn 2,500 bonus points for each additional user you add. For instance, after you get the card, you can try adding a user at this link (which may be targeted).