when trying to activate cs5.5 on your your old (or new) computer, carefully use the same adobe id/pass that you used to see your cs5.5 listed on your account.adobe.com page.
if that fails to be accepted again:
if you have an old os, your default browser must support tls 1.2, https://helpx.adobe.com/x-productkb/multi/eol-tls-support.html
to test your default browser's tls you can use , https://clienttest.ssllabs.com:8443/ssltest/viewMyClient.html
otherwise, confirm that you can connect to the secure adobe servers by reading, http://helpx.adobe.com/x-productkb/policy-pricing/activation-network-issues.html
do you see both logos after clicking "link"?
if you can and still see a connection error try these steps, https://helpx.adobe.com/download-install/kb/unable-to-reach-adobe-servers.html
if those fail, make sure you also tried the steps at, https://helpx.adobe.com/download-install/kb/common-network-connectivity-issues.html
if that fails, try https://helpx.adobe.com/download-install/kb/cannot-verify-subscription-offline-mode.html
if those all fail, white list the adobe network endpoints, https://helpx.adobe.com/enterprise/kb/network-endpoints.html
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