I purchased a boxed version of Production Premium CS 5.5 a couple of years ago and installed it on one computer. I later upgraded to CS 6 via Creative Cloud and am still a full CC subscriber (installed on two machines). My original CS 5.5 suite has been uninstalled from the original computer--but I'm not sure I ever deactivated it. Can I now install it on another computer? More to the point, can it be installed on somebody else's computer, even though the license is still in my name?
No, the licenses go together because it was a discounted upgrade... If you want to continue running your original/older Adobe version, then you have to keep it on the same two systems as your upgraded/newer release.
So if you install your previous CS5 on another machine, then it would have to go together with your CS6. Normally with traditional Adobe products, when moving software between computers you deactivate them before uninstalling. If you didn't do that, then its possible your product activation was not fully released and you may have to contact Customer Service to reset it.