I would like to have a referral program where the participant gets something for free if they refer five friends or more to Facebook who add a LIKE. Is that possible?

To track any actions in your referral program (we call them conversions), you need to paste our conversion tracking script in the HTML code of that page.  Unfortunately, Facebook does not allow access to their HTML code.  As for the LIKE or FOLLOW buttons, we track them only in our "Sweepstakes" campaigns where it gives additional entries to a participant.  It is possible to reward your Facebook subscribers when they invite their friends to register on your website.