You need to go under help menu in Lightroom 5 and choose the option to sign out if available.
Then, relaunch Lightroom and you will receive the option to sign in with your Adobe ID and choose "license this software" to license it.
unfortunately this option is not visible in my selection BUT i see that it mentions Lightroom mobile, so maybe i did not properly de-install CC?
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Yes, right. Seems like CC is interfering in between.
Would suggest you to uninstall Lightroom 5
and re-install it using this link : Download Photoshop Lightroom
Hope this would help.