From what I can see, your not far wrong. Except if your running a live CD it will be trying to restore to the root directory of the Live CD session as that's the active system. I'd mount sda5, find where it's mounted (other wise mounted it to a pre-determined dir, e.g. /media/root_drive). Now lets say that it's mounted and it's mounted under "/media/sda5". then you want to use something like the following;
Originally Posted by hub_cap
This is all based on the fact that sda5 is the partition that want for root. you'll also need to continue on and update grub etc.
sudo tar xvpfz /media/Ubuntu_2_Backup/12.04LTS-backup-2012-05-06.tgz -C /media/sda5