How can I sync my iphone5?

[Ladybird]

I get a box that says my itunes is not up to date when I connect my phone but when I click on the 'check for updates' it says it is. I know there is a newer version but my laptop wont run it because it is a mac running 10.5.8 and the Mac update also says there are no updates.
Is there any way of upgrading without it costing the earth or syncing my phone? I didn't realise that this would be a problem and am missing the music on my phone Any advice most gratefully received

[Emma]

Copy any voice messages that you want to save to your computer. I know for sure that neither Verizon nor AT&T has the capability to transfer the saved messages to your new phone - at least that's what they told me - so if it matters, do it yourself. You can really do this any time - even after you upgrade because the voice messages should still be on your old phone. But, if, like me, these are voices that you won't ever be able to get back, you might not want to take the chance that they might not be there after you upgrade. Transferring the messages is pretty easy with a simple cable that you probably already have and some free software called Audacity. The complete instructions are available in a short video on CNET.
Back up your old phone to iTunes. This happens automatically when you sync your phone to your computer. I do this pretty regularly, but my kids don't. You can upgrade without doing this, but if you sync the new phone from a backup (either on your computer or in the cloud), virtually everything about your old phone will be preserved, including your settings, all your apps, and even your camera roll - so it's totally worth it even if you've never done it before.
While you are backing up your old phone, gather up all the user IDs and passwords for all the sites you access on your iPhone - Twitter, Facebook, Foursquare, Groupon, Starbucks, etc. You will need to sign on to all of your apps again once you activate your new phone so you will need to know your user IDs and passwords. I use the CardStar app to store all my loyalty cards. All of the loyalty card information transferred flawlessly so that's one set of information you won't have to worry about.
Follow the instructions provided by your carrier to transfer your phone number. My carrier is AT&T. Since the SIM card for the iPhone 5 is much smaller than the SIM card for the iPhone 4, I didn't need to try to transfer the SIM card; I just had to make a phone call to AT&T to activate the phone service on my new iPhone.
Once you are active with your carrier, you then have to activate your phone with Apple by following the prompts on the phone. This is where you will get a prompt asking if you want to restore from a backup.
When the restore process is completed, you may want to move some apps around to take advantage of the extra row you get on each screen in the new iPhone. I had a few glitches trying to move a few apps around and getting my phone to re-sync because iTunes kept freezing during the sync process. If this happens, the trick is to close all open applications and try again. To do this, double click on the home button until you see the row of open apps displayed. Click and hold on any of the app icons until the red minus sign appears and then close each open app. Once I closed the open apps, the sync process flew by without fail each time. I had been having freezing problems ever since the last iOS update and this trick has now made syncing to my computer a breeze for both my iPad and my iPhone.
Most of my apps transferred perfectly. The one exception was Navigon, which gave me an error in the Map Manager section. After trying multiple times to access the Map Manager, I was able to solve the problem by deleting Navigon from my phone and restoring the app from iTunes. Once I did that, I had to re-download all the maps that I had on my old phone, but that didn't take too long.
Once you have the phone working and the apps organized, you will need the list of user IDs and passwords that you gathered earlier because you will need to open each of the apps that require authentication and re-enter your user ID and password. This process took me a while so if you use a lot of apps that require a user ID and password, make sure you allocate some time for this task. I was surprised at how many apps have become integrated into my daily life so spending some time re-authenticating was well worth it.