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Hi Alex jenkins, there are two ways to backup your iPhone, backup using iCloud or iTunes. The best way of backing up your *entire iPhone data is by using iTunes. For more info on how to backup iPhone, visit the link below:

How to back up your iPhone iPad and iPod touch
https://support.apple.com/en-ph/HT203977

-josh

Did you opened the GPS? You can find someone who can search the direction of your 5s.And you will got your 5s back.If you are make the backed up with icloud.you can sign in with your apple ID to find them.

believe that it is because the 5s is digital and the 4 is analog--we install blue tooth systems in cars and had to replace most of them because of the release of the 5s--older blue tooth system are analog so are not compatible with the 5s--as probably is what is your problem

The physical differences between the iPhone 5 and 5S are the camera flash and the home button. iPhone 5 has a single LED flash while the iPhone 5S has a dual LED flash. And the iPhone 5 home button doesn't have the circular ring around the button which is the finger print sensor unlike on the iPhone 5S.

Yes, the iPhone 5S can be mirrored on your Apple TV congruently with audio sound. Taken from Apple iPhone 5s Technical Specifications :

"AirPlay mirroring and video out to Apple TV (2nd and 3rd generation)"

My iPhone 5s 64GB battery life is not much better than my 4s 64GB battery life, but considering that the 5s is much much faster than my 4s I guess that's pretty impressive.

DVDXCOPY has been shut down for many years, their are a few people still selling it knowing it can't be activated. Their were a few sites that carried activation codes that worked. In all reality its not a very good program, I started out using it and switched to DVDFAB Platinum and haven't found anything it wouldn't copy, it also shrinks long movies to fit on a 4.7 DVD.