Assuming you're using Itunes 11 I'd recommend this as it's generally the easiest way to do it.
If you don't have the side bar, hold down CTRL and press S.
It'll pull up a sidebar on the left side of itunes.
Under devices you should see your device there.
Right click it, and select backup.
Now remember, your new iphone won't see your old iphones backups if your old iphone is on 6.1 and your new one is on 6.0.1/6.0.2
Once the backup is complete. You can plug in your iphone 5, find it in the same device list and select " Restore Backup"
The rest of it is pretty simple/automated.