A $5/month plan is not going to run anything but a simple/small app with low traffic but $3,000 US a month? That buys a huge (relatively) amount of RAM, clock, and bandwidth. Plenty of sites need that but they are going to be some combination of high traffic or high load… A Linode 300GB plan isn’t even $1K and it could run a fully dynamic Perl site serving 10K+ requests a second without any particular performance tuning. That's billions of pages a month, though you'll hit the bandwidth limit of that plan at around 10–20 million medium sized pages.

That said, a $5/month Nanode 1GB slice on Linode can run a modest dynamic site if the traffic is light; or a much busier one if the content is mostly static and one chooses nginx; then it becomes about bandwidth. I will underscore that while apache is the most flexible and featureful webserver, nginx beats the pants off it on performance metrics.

Update, coupl’a typoeses.

I know huge businesses which spend a fraction of that on hosting. Conversely I've know of small business being overcharged for their needs, in some cases due to the developers producing awful code. Without knowing what you're doing and how you're doing it, I'd still be inclined to say you're being overcharged, purely on the basis of experience.