are there sites that pay you $5 a week if you don't get many referals?

I think there are, but you need to invest some money in too. I've recently invested for rented refs in neobus=x and it got me my payment for the first time in 4 days only.

I don't know of any one site yet. But you can probably aggregate several sites to get $5 a week. The only drawback is that, for such kind of money and without much referrals, you'll find yourself exerting a lot of effort trying to earn your target income. Getting referrals (and I recommend offline referrals) is still a good strategy for earning online. Of course, it does not necessarily mean that it will be easy. However, once you have several referrals, you can expect to earn much with very little effort.