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.