How do I sync my iPhone5 to my calendar and contacts which is Outlook on my PC?

You can sync them using iCloud by syncing your computer with your iCloud account and selecting to sync your Mail, Contacts, Calendars and Tasks with Outlook on the iCloud control panel for windows, as explained here: http://www.apple.com/icloud/setup/pc.html. This requires Outlook 2007 or newer.

You can also sync with iTunes if you prefer by connecting your phone to your computer, going to the Info tab of your iTunes sync settings and selecting to sync your calendar and contacts with Outlook, then clicking Apply to sync (requires Outlook 2003 or newer). Suggest you back up your contacts (such as by using an app like My Contacts Backup) before doing so. You should get a merge or replace prompt; choose merge.

iTunes 11.0.1.12 does not seem to allow synching with the iPhone 5. The sub menu's under Devices are greyed out. I'm trying to sync my outlook contacts to my iPhone.

If it's grayed out that's an indication that your phone is not being detected by iTunes. When you connect your phone to your computer and open iTunes, does the name of your phone appear on the upper right (or on the left side if you have View>Show Sidebar active)? If not, go through the troubleshooting steps here: iPhone not recognized in iTunes for Windows, especially 1-6 at the bottom.

Thanks, the name of my phone does appear in top right.

I have synched by using iCloud to upload from Outlook, and then to my iphone. problem now is my Outlook is corrupt, and wont send anything from my Outbox.

Wonder how much testing Apple did before releasing?

Don't know about Outlook, but if iTunes is not recognizing your phone, go through the troubleshooting steps in this article: iPhone not recognized in iTunes for Windows