I have been hosting my sites with www.hostquack.com for over 4 months now and they are great. 5gb space 50gb bandwidth for only $4.95, just what you are looking for. They allow unlimited addon domains, my friend who is also hosted there has over 30 domains added to his shared account.
$5 isn't very much or at least that's what people think around here anyways. Once you've found a host that meets your needs in terms of space and bandwidth do make sure to looks for coupons on the Internet or even on webhostingtalk offers forum. It is just silly not to use a coupon of some kind.
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Check offers, compile a small list, work through each host, submit some sales questions etc, make the list smaller, then make the final decision. There are plenty of hosts who offer what you're looking for.
Your budget is fair, but you may not get top notch support. Let me ask you this, how important is uptime to you? Are these personal or business sites? I might would up the budget just a bit for a better quality host.
I think you can definitely get the package you are looking for within the budget you have. Obviously you need a host that will allow unlimited domains if you stay within the quota of your disk space/bandwidth.