Transferring music from iPhone 4 to iPhone 5?

I was wondering if anyone could help me with an issue that has bugged me for a very long time.

Is there anyway you can use iTunes to back up your personal music collection on your device and than transfer it to your new device say 4s or 5?

I know in iTunes you can sync your playlists to your device and then sync back to another device but I use the 'manual mange music option' as I prefer the drag and drop option from the old iPod days.

If anyone has a solution for this or even an external programme that can do this I will be very grateful

iTunes will only transfer the music if you don't have the manual music and video button checked.

To put it into better context, the music in my iPhone is no longer on my PC. If i did a standard backup, iTunes will not backup music not purchased from iTunes. It also can't restore the music from my PC as its no longer there.

So is it possible to transfer the music from iphone (including playlists) and then transferring this a new device?