Adobe master collection CS5.5 and CS6.0 activation count full

The activation servers haven't been shut down, but if the two-activation limit is reached, one of them has to be deactivated, and that can only be done from within the application (Help > Deactivate).

Adobe have changed their policies, since 2014. CC applications can be remotely deactivated from your web browser. 

Up until recently, they would give you a new activation if you called them and explained why, such as hard drive fail. They stopped doing that about a year ago.

@anttim62180250 on your new computer? It is highly probable that you will encounter compatibility problems, crashes, or features that simply don't work correctly on the new operating system with compatibility issues with Windows 11. CS5.5 came out in 2011 and CS6 in 2012. Adobe officially ended general support for both of these suites several years ago, as they shifted their business model to the subscription-based Creative Cloud.

You will need to have serial numbers and Adobe ID. But, be advised, many users have reported that Adobe Support is no longer able to or willing to reset the activation counts for these very old, unsupported products. Instead, you may be told that the activation servers have been shut down and that the only option is to upgrade to a Creative Cloud subscription. While this isn't a universally confirmed policy change and may depend on the support agent you get, it's a possibility you should be aware of and not get your hopes up. 

Because I am not an customer support, and this forum is sometimes read by Adobe Employees, and sometimes not, be patient and good luck