CC says I've got Lightroom5 and it's up to date. Try just downloading off the Adobe site and it says LightroomCC is downloading but nothing appearing in DownLoads.
OK, the CC-> Preferences "Sign out- Sign in" trick worked. Or at least Lightroom CC has appeared in the CC window as a software that can be downloaded.
I successfully downloaded the software, then clicked on it. Came up with a quick LR 6/CC Splash Page, then the Splash Page disappears and LR is not loaded.
CC->Preferences "Sign out-Sign in" trick worked for me as well. MacBook Pro running 10.10.3 Yosemite.