Dreamweaver CS5 serial number

Did you deactivate Creative Suite from your previously installed devices first?
That's critically important because your individual license has a strict 2 time activation limit. Remote deactivation of legacy apps is not possible.
- https://helpx.adobe.com/download-install/kb/activate-deactivate-products.html
- https://helpx.adobe.com/download-install/kb/activation-deactivation-help.html

If the old devices are dead or no longer in your possession, you're stuck. You won't be allowed to activate CS on another device.

CS5 or CS6 REPLACEMENTS

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Creative Cloud Bundles & Single Apps for mobile, web & desktops
https://www.adobe.com/creativecloud/plans.html

OTHER OPTIONS:

-- Codespaces (free, browser-based) - https://github.com/features/codespaces
-- Notepad++ (free) - https://notepad-plus-plus.org/
-- Nova (Mac only, formerly called Coda) - https://nova.app/
-- Pinegrow - https://pinegrow.com/
-- Sublime Text - http://www.sublimetext.com/
-- Visual Studio Code (free) - https://code.visualstudio.com/
-- Wappler ~ Visual Web App Builder - https://wappler.io/

ONLINE SITE BUILDERS:
-- Squarespace - https://www.squarespace.com/
-- Webflow - https://webflow.com
-- Wix - https://www.wix.com/
-- WordPress (open source) - https://wordpress.org/

Hope that helps.

If you did not deactivate the software on the old computers prior to moving to the new one then unfortunately there is nothing else that can be done. The system activation counts can no longer be reset by support and your only option would be to subscribe to the latest release.