I just bought an Iphone 5 and I cannot connect to Itunes to update some apps.
I don't quite understand what you mean by this. Do you mean:
a) I cannot connect to iTunes on my iPhone 5 at all, ever
b) I can connect to iTunes but no apps will update
c) I can connect to iTunes but some app update and others don't
I can connect my laptop to the Itunes store and update which I have done. I cannot get there with my new Iphone. I am not running Itunes 11 yet on my computer. Help me please.
This part I understand. You have a workaround that works, but still have the problem.
While I don't think it will solve the problem, you should update the iTunes on your notebook to the latest version available.
As for the issue: is there any possibility that the apps that won't update were purchased under a different iTunes account? Is there any possibility that you have two or more iTunes accounts tied to the same email address? Is there any possibility that some apps were purchased from a different country's iTunes store?