Rechnertausch

you can leave everything cc on the old computer (and continue to use it).  unless you're selling/giving it to someone else*.

just install the cc desktop app from here https://creativecloud.adobe.com/apps/all/desktop?action=install&source=apps&productId=creative-cloud on your new computer and use it to install your adobe subscription and trial programs.

if you have trouble downloading, use the alternative download site at page bottom here, https://helpx.adobe.com/in/download-install/kb/creative-cloud-desktop-app-download.html

*to remove everything cc from the old computer (if that's what you want to do),

uninstall every cc app including preferences, https://helpx.adobe.com/creative-cloud/help/uninstall-remove-app.html
then uninstall the cc desktop app, https://helpx.adobe.com/creative-cloud/help/uninstall-creative-cloud-desktop-app.html
clean your computer of cc files per http://www.adobe.com/support/contact/cscleanertool.html
check for, and if available, update your os
restart your computer (don't skip this)
reinstall the cc desktop app, https://creative.adobe.com/products/creative-cloud.
if you're unable to install the cc desktop app at this stage, use an administrator account (solution 4 here, https://helpx.adobe.com/creative-cloud/kb/creative-cloud-missing-damaged.html)
use the desktop app to install your cc programs/trials

DE-activate on old http://helpx.adobe.com/x-productkb/policy-pricing/activation-deactivation-products.html

Download Cloud Manager to install all programs on new https://www.adobe.com/ie/creativecloud/desktop-app.html
-https://community.adobe.com/t5/get-started/how-to-activate-your-adobe-software/td-p/9636861?page=1