Keep version 5.6 64 bit or delete it, after updating to 2015 release?

I am very confused.

I purchased the Adobe Creative Cloud (Lightroom and Photoshop) a few months ago, and have been using both without problems. When I got a notification for updates, I downloaded them.

Now I have noticed the are TWO versions of Lightroom in my computer:

"Adobe Photoshop Lightroom Version 5.6 64 bit with Camera RAW 8.6" and "Adobe Photoshop Lightroom CC 2015 Release, Camera RAW 9.0"

I also have "Photoshop CC 2014.2.2 Release 20141204.r.310x64"

I think I have been using both versions of Lightroom for a few days, and having made a few tests, it appears to me that both versions do not talk to each other.

What a mess! So what should I do? Am I to uninstall version 5.6? Keep both? Use the old version?

I hope I'm not buying both versions, either.

Luis