Q: Attempting to set up new computer to Sync with my Iphone5. Downloaded I tunes but do not find way to authorize this computer or sync

You should be able to authorise your account via the Store drop-down menu at the top of iTunes- if you are using iTunes on a PC then try pressing Alt-S and the Store menu should appear (or control-B and the menus should show, they are hidden by default on iTunes 11 on PCs) e.g.

If you syncing to that computer for the first time then you may also find this page useful : https://discussions.apple.com/docs/DOC-3141