I've seen .5 gallon reefs before. It had a couple of hermits in it and one or two polyps.
That said, I wouldn't recommend it at all. Especially seeing as you're new to saltwater.
I've had my 36g salt tank up for a year now and I've just started to add corals. Mainly because the tank hasn't been balanced enough in my opinion to support anything more than fish.
One thing I can't stress enough is to plan, plan, plan! Do your research, and lots of it. It will reward you in the long run.
Setting up a 5 gallon reef is going to be hard. Because it's such a small amount of water, a greater percentage of the water will evaporate than in a bigger system. This is fine if you can keep up on topping water off and dosing properly...But because you're new to this, I wouldn't start a reef in anything less than 10 gallons.
About what to buy, the tank obviously

, if you go with corals, there are different lights you can get for different types of corals. Lps corals need stronger light and flow than sps and softies. So because you haven't specified what types of corals you want to keep, I can't help you there. I have a 132W power compact light on my 36 gallon, and my soft corals thrive. Some people say you need a protein skimmer for a reef, while others say it is detrimental to it. I personally don't run a skimmer, and like I said, my corals have been fine. If you are dealing with some more delicate species such as Acropora, I think it would be wise to invest in one. Personal choice though. A powerhead is needed to create flow in the tank, and you'll want a stronger flow if you have corals in the tank, so look up on those once you've decided what corals you want.
Now, when you set up your tank, you need to take it slow. One day put the water and sand in...Then maybe the next day add a piece of live rock (which can run you anywhere from $2-$10 a lb.). This will act as your biological filtration and is probably the most important part of your whole tank set up. If you go with a 5 gallon, I wouldn't put any fish in it, so next, probably 2 weeks after that to allow it to cycle properly, I would add some hermit crabs and snails, etc. Personally, I would wait until about 2 months to add any corals, and for them you will want to pick up some fragged corals. They come on little pieces of rocks, and instead of running you $50 for a coral, get a frag for $5 and then grow it yourself! Much more exciting

Anyway, I know I've missed a lot, but once you start setting your tank up then I can help a bit more with the specifics.