Xcode 5 update, why am I stuck on Xcode 3.2.6? I'm running Xcode (downloaded from the Mac App Store) on my MacBook Pro running OS X Mavericks.

The weird thing is I am running version 3.2.6, yet Xcode claims to be up to date. There are no updates in the Mac App Store.
You may have Xcode 3.2.6 from an earlier installation and are running it. Note that Xcode 3.x being a pre-MAS (Mac App Store) version, installs into the /Developer folder (by default, although it can be installed elsewhere too), whereas the Mac App Store versions (from Xcode 4 onwards) install into the /Applications folder. To run Xcode 5, make sure you're running the application from /Applications. You can also use Spotlight to find where Xcode 3.2.6 resides on your system.

If you wish to uninstall the older version (Xcode 3.2.6), open Terminal.app and uninstall it using the command:

sudo /Developer/Library/uninstall-devtools --mode=all