Don't know exactly why the normal update doesn't work, but now, after re-installing the app completely, everything works fine for me (also the new updates from the 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:
This is most likely (well I presume) because you installed the application on another apple ID, the one it is asking you to enter. There is no way around it other then to enter it.
Best Answer
Unfortunately, I got the same problem some times ago, when, after upgrading to El Capitan, I couldn't update to Xcode 7.1.1.
To solve this issue, I did the following:
Don't know exactly why the normal update doesn't work, but now, after re-installing the app completely, everything works fine for me (also the new updates from the App store).