How To Transfer Music From Old 3GS To New IPhone 5s Not Using ITunes

i want to take all my music off my old iPhone 3 and transfer it to my new iPhone 5s not using iTunes i can't get into the old 3g as the screen swipe is not responding,after my child played with it for 5 mins dont know what she has done[but will to turn off?] but when i plug it into my mac book air i can see/play all the music,if i try to use i tunes i say it is synced with a different library on another computer which was years ago and long gone ,this was a lot of old cd i had bought through the years and had them put onto the 3g