Adobe Web Premium CS5

I do not have access to the old computer...

By @artur_1497

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You've reached the end of the road for this product.  Without access to previously installed devices, you can't activate on a new machine.  Sorry. 

Perpetual means you have a license to use it for the life of the software. At purchase, the shelf-life was 3-5 years.  After which you were expected to replace it or use at your own risk of failures.

No computer product lasts forever. That's not how technology works.  CS5 is 15-years-old. You got your money's worth and a good deal more.  

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

there's no longer any other way to deactivate than to use your inaccessible computers.

You are allowed 2 activations... if you did not DE-activate previous installs you may not proceed

For serial number programs you may download only if you bought direct from Adobe
-Log in to your Adobe account and click this link https://account.adobe.com/products
--IF a download is available there will be a Download button under the program name
---as always, write the serial number in a text file AND copy that text file and the
---download file(s) to an external drive (or two) to be sure you always have what you need
---since Adobe DOES sometimes remove very old downloads from their file server
-if you did not buy direct from Adobe you must find your original install
-if you have an Education or volume license you MUST use your original media
--the link for an Education or volume license download is not available at all
-if you bought a disc and don't have a drive you will need to buy an external USB drive
-if you bought and lost a CD/DVD disc Adobe does not provide a replacement
-if you bought a download from a 3rd party vendor you will need to contact that vendor