Photoshop CS5 – Seriennummer auf neuem Rechner aktivieren nicht möglich

For your old computer

TLS 1.2 is now required to connect https://helpx.adobe.com/x-productkb/multi/eol-tls-support.html
-If you have Windows 7 be sure to do the EASYFIX.MSI in step 2 of the above link
-test your browser https://clienttest.ssllabs.com:8443/ssltest/viewMyClient.html
-http://helpx.adobe.com/x-productkb/policy-pricing/activation-network-issues.html
-https://helpx.adobe.com/download-install/kb/unable-to-reach-adobe-servers.html
-https://helpx.adobe.com/creative-cloud/kb/troubleshoot-download-install-logs.html#error113
-https://docs.microsoft.com/en-us/mem/configmgr/core/plan-design/security/enable-tls-1-2

the two issues are independent.

the first indicates your deactivation failed to be communicated to adobe's servers.  this is a common problem that's sometimes caused by the host computer not meeting adobe's security requirements.

the second indicates you may have an enterprise version of cs5 which was time- limited for activation.

@S460785105g29 The issue you are encountering—both the "serial number has already been activated on two computers" and the message that "the time limit for activating Adobe Photoshop CS5 Extended has been exceeded"—points to a significant change in how Adobe handles older, perpetual licenses... Adobe is now on a subscription base workflow. 

CS5 is a retired product and is no longer officially supported. Support ended a long time ago in 2014, that's 11 years ago. This means that Adobe no longer provides customer service or technical assistance for installation, activation, or troubleshooting for this version. The second part of your error message, "the time limit... has been exceeded," strongly suggests that Adobe's activation servers for CS5 have been retired or are no longer maintained for this purpose. In the past, Adobe Support could manually "reset" your activation count on their servers. But, because CS5 is an unsupported, end-of-life product, Adobe no longer performs these activation count resets for this version.

If you do a Google search, some users report it can run on Windows 10 or 11. However, you might encounter glitches or need to run the installer in Compatibility Mode for an older OS. You could, although, I never tried, to install an older version of Windows (like Windows 7) inside a Virtual Machine and then install and activate CS5 within that virtual environment. Be cautious of using any serial keys found online that are not your original purchase key, as these are unauthorized and may not work or could lead to instability, security or legal issues. Use only the serial number you legitimately purchased.