It really depends on your site. Is it static vs dynamic, resoursage usage, etc.
"Shared Hosting" can technically handle 5000 daily visitors if it is on a strong enough server, and there are not many other clients on that server. However your not likely to find a host that will allow a shared customer to use that many resources.
If your at 800 a day, it is about time to go ahead and plan your next step up. If you get a spike in traffic one day, you could find yourself in a bad spot.
Once you out grow shared hosting, a VPS is usually the next step. This is still a shared machine, but you get your own dedicated resources.
The wonderful thing about VPS's is they can scal instantly. If you move your site to VPS plan "A", and your traffic increases, simply ask your host to upgrade you to plan "B" and you have the extra RAM/CPU/Space without having to physically move your sites to a new hosting machine!
