Hello,
At 5k visits a day you really need a dedicated server. Here at Shape 5 we switched to one early on as 1k visits a day, of course all the downloading adds to that for us. But 5k on a shared is huge. Especially because who knows what all the other accounts on that server are bringing in.
You might want to check out
http://www.softlayer.com/ they have some very nice and affordable dedicated servers. They are actually the host we use here at shape5.com
Hope this helps!