Every 'smart' phone is closed source to some degree and so, insecure. The least closed would be an Android running Replicant with only the modem closed, next would probably be a Galaxy running Cyanogenmod. iphone is pretty much a closed and controlled shop but is if not rooted then possibly more secure... just less private.
It depends what privacy you want and what you think is the biggest threat. Personally if I had bought an iphone anyway I would trust Apple but hesitate to trust the apps.
So, up to You, how to secure yourself, dealing with bitcoin and using Iphone 5 ? Or, maybe, it is worth not to deal with bitcoin, using Iphone ?
My gut feeling is that security is good on an unrooted iphone but privacy is poor. If you are worried about someone hacking your phone then the iphone is
probably good. If you are worried about your taxman looking at your phone and then billing you then it is
probably a bad.
This is my gut feeling regards closed source things.
So the answer is - it depends. You are in the hands of Apple, you either trust them or you don't, it's not for me to say. Personally I trust them but perhaps other people would be more paranoid that somehow Apple might delete the Bitcoin app from your phone somehow (possible?) - does that happen if an app is pulled from iTunes?