There are well over 100 pages of posts on the Apple Forums regarding this problem. I am on my third iP5 - haven't activated it yet - that comes later tonight. The general issue is that when my other apple devices are able to get 10 - 15 Mbps download speeds over WiFi, the iPhone 5 can only muster about 500 - 756 Kbps. Some devices can't connect at all. With my original iPhone 5 I waited for 20 minutes for Instagram to update. Can't watch YouTube videos, email attachments don't download, etc.
I was lucky enough to get a smart and seemingly honest "Advisor" on the phone the first time that I called and he's been able to help me through this problem. He said that Apple does know that there is a problem, that the engineers have not gotten it nailed down to a specific hardware / software / combo issue. Of course, there's a question as to when Apple will officially admit that there is an issue, and then, when will it get fixed...!