I Phone 5?

My sister has so far had two replacements of her I Phone 5 and both have turned off randomly, the music plays and stops at random, and freezes, cuts phone calls. The most current replacement just shuts off and doesn't turn back on for days. My sister doesn't want to get an Android (which I suggested) because she doesn't want to lose he massive library of music.

I really would like some help either fixing the phone or finding a way to back up her music so she can finally get an android.

Thanks in advance.