How do I re-install Photoshop CS5?

In the absence of a compatible older computer that supports legacy (10+ year old) software, your original installation disks & valid serial number that you received at purchase, and an optical reader that can read those disks, you'll need to replace Creative Suite with modern software.

MODERN OPTIONS:
Photoshop Elements or Premiere Elements (approx $100, no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Camera Raw
• Lightroom on desktop, mobile and the web
• Lightroom Classic
• Portfolio website + hosting
• Adobe Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).
• Free upgrades for paid subscribers

https://www.adobe.com/creativecloud/photography.html

Premium Adobe Express ($10/month).

• Creative Cloud Express app (web and mobile)
• Premiere Rush (video editing on desktop and mobile)
• Photoshop Express (mobile)
• Spark Video (mobile)
• Spark Page (mobile)
• Adobe Portfolio + hosting
• 100 GB of cloud storage
• All premium templates and design assets including the collection of over 160 million royalty-free Adobe Stock photo collection.

https://helpx.adobe.com/express/using/express-overview.html

Creative Cloud All Apps (51 + apps & services) and Single App Plans
https://www.adobe.com/creativecloud/plans.html

Hope that helps.

ok, i see you edited your message and that was more informative.  if that was accurate, you can get one type of cs5 installation file here, 

https://prodesigntools.com/adobe-direct-download-links.html

follow the directions (esp, step 1)

save the install file. it may not remain online.

thank jim @ prodesigntools.com

you'll need to reinstall and activate your photoshop version using the installation file and serial number that matches that file.

and, if your version is cs4 or older, you won't be able to activate because of a problem on adobe's end.

if you want more help/info, what ps version and what os version and why are you trying to use offline activation (which introduces another problem)?

You probably can't but let's start with some details. Photoshop has not had verification codes for years. What version are you trying to install, and do you still have the disk and serial number?  Don't tell us the serial number. Warning: fake Adobe reps may contact you to sell you a fix: real reps have nothing to sell. 

DEAR ADOBE,  i have a VERIFICATION CODE FOR ADOBE PHOTOSHOP WHICH I LOST  from MY PC when it was CLEANED FROM A VIRUS,  HOW CAN I RE-INSTALL my 'PHOTOSHOP'PLEASE?  donreade@bigpond.com

CODE: 890059 on 21 APRIL 2020