How to transfer my music from my iPhone 3s to my iPhone 5?

I just purchased the new iPhone 5 and when I did I also had to download the new iTunes. When I did this it deleted all the songs except the purchased ones from my library. The songs are still on my old iPhone but when I try home sharing or anything like that it won't let me move my music.

Itunes

Ya that's what I hate about iTunes, you can transfer songs from iTunes to iPhone but you can't transfer songs from iTunes to iTunes just google for a program to extract the music files from your iPhone 3GS to put it onto your iphone5 that's what I did

IPhone Transfer Platinum is the professional tool to help iPhone users to transfer any files like music/movie/Pictures/TV Shows/Podcast/iTunes U/eBooks/Camera Roll/Ringtone/SMS/Contacts/Voice memos/Camera shot between any two Apple devices including iPhone3s and iPhone5.