How to download something onto your iphone using itunes?

I have a Mac Version 10.5.8. I know it's old but I can't afford anything else new. So recently I received an iphone as a present from somebody. I want to download my old songs onto my new phone using itunes but my computer is too old to download the new version of itunes. Can I download the songs using itunes even though my computer is old and if so, how?

- You should be able to download the songs by Authorising your device. ( find how to do this with apple support )
- Plug in your iPhone
-Erase and sync then transfer purchases.
-At this point your music should be downloaded from your iTunes account and in your library, so just sync the device.