Although I don't know any providers off of the top of my head, it's quite possible that you can fetch a low end VPS at that price point. However, don't expect a control panel or anything more than 64 megs of RAM or so.
I have to agree with the above. And if you find one VPS for $5, you can almost be assured that they are overselling services. I'd suggest setting your budget a bit higher. It's always good to know what specs you need.
No VPS plans for $5 or even $10 per month. Sorry that I should say that and please do not offend, but you obviously do not understand the VPs technology and what does guaranteed resources mean.
Host Color★Colocation, Dedicated&Europe Dedicated Servers★since 2000 U.S. Data center★★90 miles from Chicago Network ★ AS46873★★Level 3, Cogent, Hurricane Electric, Retn.net, Midwest Peering
24/7 Support ★★ 1-574-367-2393; Skype: HostColor
Okay, partly for the sake of denying everyone else that a $5/month vps is impossible, you should probably check out lowendbox (google it) which specialises in these types of offers. However, you may want to check around for reviews of some of these providers here as some of them may be unreliable.
Do note that of course these plans are _very_ low-spec.
We really need more information as to what your needs are (Ram, Disk, Bandwidth, what you plan to use this for, etc...)
While I agree with everyone's sentiment about $5 VPS accounts in general, I think it really depends on what it is that you are trying to run on it and what your expectations are. I have a number of accounts with top tier hosts (for example Knownhost) and a number of accounts with budget providers (ex: Ramhost.us). I have very different expectations with each tier of host and I'm quite happy with both.
While I believe that quality providers like Knownhost are worth their weight in gold, I think there is a market for low end VPS accounts with minimal resources. In my months with Ramhost I've had exactly two minor issues that were resolved about the same time I noticed them. Looking at my logs at about the same time frame of time used I had more issues with a couple of much more expensive "top" hosts then I have with Ramhost. Pretty good for a less then $10 VPS.
I'm not saying that this type of VPS is good for everything you may want to do on them, obviously you need to be realistic about what you can run on them. But I have several uses where this type of VPS is a much better fit then a $50 VPS. I don't expect them to have the same response times as Knownhost or Wiredtree, I don't expect a $5 account with 1TB of bandwidth, and any support I get is a bonus.