Remove Apps from background memory. Press home button twice quickly, in new row of icons at bottom of screen, tap and hold on one icon until Red Minus Sign appears, tap all the Red Minus Signs. Then Reset, hold both Home and Power button until the iPhone restarts itself, ignore the "slide to power off", let iPhone restart itself. See if better. If still problem, Restore iPhone Firmware with iTunes on computer. If still problem, make Genius reservation and take iPhone to Apple for resolution.
The reset didn't work, but a DFU firmware restore did. I went to the Apple store and they ran a diagnostic on my phone and the tech said there was an error there that he'd never seen before and the solution was to restore the firmware. There are 2 types - the usual type that we normally do at home when connected to iTunes and the one's they do. He said make a back up, connect the phone to the computer and then press and hold the home and power button. The screen will go black after approximately 3 seconds. When it does, release the power button and continue to hold the home button. This will start performing a DFU firmware restore.
Once it's complete, just reload your back up.
The difference between the two restores is the DFU wipes and reinstalls the firmware whereas the regular restore only repairs.
Hopefully that can help someone else. After performing that I've had no issues.
I have this same freezing problem, and it occurs in diverse apps as well as in the iPhone settings themselves.
I notice MANY complaints in the Apple Support Communities about this same freezing problem on iPhone 5s running IOS 6.01 and even the brand new 6.02. The standard response from the "experts" in the support community here -- to reboot or restore the iphone (or visit the apple store or call Apple Care) -- rather misses the point, in my opinion. So many iphone 5 users should not be having the same exact problem!
Instead of band-aid replies to reboot and restore or get Apple tech support involved, we need an actual lasting fix to this systemic problem, so the freezing stops happening for all of us.
The real question is this: What explains this too-common freezing problem on iPhone 5 running IOS 6x?
I believe that Apple has screwed up, plain and simple, by putting out a device and OS that has not yet been properly vetted. Seems that Apple has been doing this a lot lately (e.g., OS7x Lion, the Apple Maps app), and I suspect this is an internal Apple culture issue -- a pushback against the perfectionism of the late Steve Jobs, perhaps. If so, that's too bad for us devoted Apple product users as well as Apple's investors, quite honestly. Apple Corporation itself needs to reboot and restore its "insanely great" standard of excellence!
Meanwhile, I am still looking for a reliable and permanent way to stop my brand new iPhone 5 from freezing constantly.