If you have just made a purchase then perhaps you need to sign out of the CC Desktop app, using the Gear / Preferences / Account tab. Then sign back in.
Whether you need to uninstall would depend on whether the LR 5 you installed came from the serial-number installer or the CC-installer. You can uninstall the LR5 that you have, log out of CC Desktop, then make sure you're installing the LR5-CC from https://creative.adobe.com/products
