OK, here is one way to begin something out of your 5 big dollars! >>
There is a member on BHW who is giving away free hosting (I think it is free for 6 months). So take it, and before that buy a discounted domain (sometimes you can even get a .com domain for less than $1). Now use both and install free Wordpress on it. Create a blog or any other site and make it work for you. What kind of website will produce some income for you is for you to decide.
There are other hosts who offer free web hosting and without advertisement,s but it also comes with some limited services, for example, you won't get instant support/help from them. But otherwise for free hosting, they offer a lot of good features for people like you (and me too

) who have money constraints but need a hosting urgently.
If you wish to go the above-mentioned way, then our BHW forums are filled with useful knowledge and methods which you can select and turn your new site into a great one. It will take some time, but anyway $5 will at least give you something to begin with.
Remember, for getting any such online success, you need targeted traffic to your site. So begin learning how to achieve that flow to your site. Content is a big factor in achieving any success, so...
Another way... if you know of some local manufacturer who produces good low-cost product then you can sell those products on eBay. I began by finding a good manufacturer, and took images of the products he made, then I used eBay to advertise those products for a good profit margin. Luckily I got many customers, and I bought the required items then (i.e., after I got orders), and sold them to these customers. There was very little investment involved and my money didn't get tied up for long durations because I purchased only the required items which were already in stock at the manufacturer and the purchased stock was immediately delivered to my customers. So you can try on these lines too.
If you require more investment, then monitory help from any friend or relatives can be availed for your needs as an individual seller, or even a bank can provide you with the investment if you open some kind of company which doesn't cost much investment to open on paper at least. Google-search for the information, or visit the nearest bank and request the information.
Thirdly, focus on what you want to do without thinking of the small amount you have on hand, rather than worry about what you can do with $5 only. You may even get an idea and can begin something huge without spending even one single cent! Widen your horizons infinitely and in all direction, and don't let them shrink to the size of a money bill you have in your pocket. Ultimately, it's always the quality and not the quantity especially if it means a small/tiny size, that counts in the world around you!