problem mit der Aktivierung von adobe cs5

Ioannis,

In addition to what Bill said, I am afraid that the only (safe) way to bring CS5 over, if at all possible for other reasons, is to clone the (main) harddisk from the old PC.

And if you actually managed to deactivate CS5 on the old one ("I have already deactivated the old computer without success."), I am afraid you are in real trouble. Can it still run there?

You can have a CS version activated on two PCs, so a deactivation would have been unneeded.

I really hope the contact suggestion by Bill can rescue you.

Here is a HelpX page from last year,

https://helpx.adobe.com/download-install/apps/troubleshoot/licensing-activation-issues/cant-sign-in-creative-cloud-2018.html

and a probably long outdated thread from 2019 specifically about CS5,

https://community.adobe.com/t5/adobe-community-experts-discussions/just-to-be-certain-i-m-absolutely-clear-about-adobe-support-policy/m-p/10827644#M24649

Unfortunately, the activation server for CS5 has been shut down. You can contact Adobe at https://helpx.adobe.com/contact.html but it is unlikely that you will get any help as CS5 is no longer officially supported. Besides, it is also unlikely that CS5 will even work on a new modern machine. If you have a brand new machine your best option will be to get a subscription to Creative Cloud.