How to move music from old iphone to new iphone?

I have music downloaded directly from itunes onto my iphone 3 and I have just got the iphone 5 and want to put that music on my new iphone. I can't seem to get any of that downloaded music onto my new iphone. Surely I don't have to buy all the music again?
Any help would be much appreciated. If the answer isn't resolved on here then i'll ring apple support.

Added (1). Sorry I should have been more specific, the music was downloaded from my itunes library on my phone not a computer. I can't seem to get the music from my old iphone onto the computer either.

Added (2). Looks like I've found out how to do it. I ended up going onto itunes on my computer and went onto the itunes store, checked my purchased items and have just downloaded them to my computer.

Sync them both with the same iTunes account.

Back up your old iPhone and restore your new phone with the old iPhone's backup.

The new iPhone needs to be setup with the same email address as old, if you have used the same details to setup then when you visit iTunes it should say purchased for all tracks you had before, if you have a pc/laptop use iTunes on there to transfer without having to redownload

If you've purchase music from iTunes you can do this two ways.

Drag and drop on iTunes on the computer.

Or,

Open the iTunes app, tap more, tap purchased, tap music, tap all songs, then download All your songs.

Hope this helps

  • Move All data from old iPhone to new? I have an iPhone 5 on iOS 7.1, and I want to move everything onto my new iPhone 5s on iOS 7.0.4 Is there any way to do this without *updating*? I mostly just want to transfer over the messages/contacts/ photos/app game data, notes I made a full backup but it does not seem to add anything to the 5s when I restore. I believe I saw a message once saying the backup may not work due to using an older iOS
  • I can't move music from my iTunes onto my new iPhone? I recently just got the new iPhone 5. I'm trying to move my music from my iTunes library into my iPhone, but for some reason, the device won't appear on the side like it usually does (when you plug in a normal ipod/itouch, the device appears on the side where the library, store, playlists, and genius categories are located).So I can't move any music because it won't come up… Help?
  • How to transfer new music to iphone without deleting old music? So i lost all my music on my hard drive but it is still on my iphone. Is there a way to put new music on my iphone without it deleting everything else on my phone, seen as its not on my mac
  • How to transfer music off my old iPhone to my new laptop without loosing the songs off my old phone? My computer died therefore I have music only on this certain I phone. I have since got a new laptop, new phone and new music but don't want to loose all the music off my old phone. Hope I'm Making sense.