Unless you have very high credit-card spending, you may be out of luck. The miles benefits are mainly for frequent fliers and frequent stayers at hotel, since you do not fit this profile, your best option would be the credit card route. 5 tickets to Europe should be somewhere around 350-400k points (and availability might be an issue), you can probably get 60k by credit card sign-up bonuses, but you still have to earn another 300k points. I would think it would be easier for you to save up $3500 or so to pay for the airfare.