This is an issue that is being discussed a lot in the Apple forums. Consensus is that it is happening on wifi networks that use AES. I have verified it on a friends phone that has the problem by changing network security to not use AES, and her new iPhone 5 works fine. Her iPad, her computer and her old iPhone 4 do not have the problem on her network, even with AES used.
No one seems to know it this can be fixed with an iOS update or not, and many have exchanged their iPhone 5s and still see the problem. Hmmm