You have to come outside of the three main tourist peaks, and you have to hunt a bit to find the $5-rate. The touristy weeks are all based on locals going to the beaches, and that happens usually around Christmas and the New Years. Then later during Carnaval, and then finally during "Semana Santa" (holy week). But for the other 48 weeks of the year, space is available...

If you are willing to spend $10 a night, then your choices expand. Most of the low-end places are in the $7-$8 per night per person range. ($5 places do exist, too. For instance in Araya, a seaside town near Cumana, three of the four hotels there are all priced at $5. The last - and most luxurious, if that is the word - is at around twice that).
But don't look exclusively to the hotels or the posadas, as the Bed & Breakfast places are known here. Look into the private market too, where home owners rent out a room in their house or an annex in the garden, or, as it were, in many cases the pool cabana. This is a way for them to get some extra cash income, tax free. And you get cheap accomodation near the beach.

Or ON the beach: One way of finding a place to stay is simply to walk along the beach. Before you know it, you will stumble into a local. He probably lives there. If you speak a little Spanish - which is the language here - then you are well on your way to finding a place to stay. Because either he already has a small cabana-type bungalow on the beach, for renting out to tourists. Or else he knows someone who does. It is very common here. You can't walk on any of the beaches in the built-up areas without seeing these small guest houses. A lot of them are for rent.

Renting a room is the cheapest. From between $5 and $10 per night is the fair rate. Renting your own bungalow or a whole villa is a MUCH nicer option. Also more pricey. But probably worth it, especially if you are staying for a while and if you are a group.