How do i transfer my itunes onto another computer that is authorised

My Itunes account is on a computer which has now broke. I have authorised this computer to share the account. I have all my library on my Iphone. However when I plug it in it says 'this iphone cant be used as it needs Itunes 10.5 or later' is this the phone or the computer? Ive tried to find a way of upgrading both but I just cant do it.