Unable to download Lightroom 5 onto new pc

If you're still stuck, you can try downloading from

https://prodesigntools.com/lightroom-5-ddl-comparison-vs-lr4.html

LR5 is end of life and no longer supported.  Public links to downloads were taken down. Customer care agents cannot help you unless you have a paid Creative Cloud subscription.

Creative Cloud Photography Plan (approx $10/month for 1 year subscription). Everything digital photographers need and more.
https://www.adobe.com/creativecloud/photography.html

For CS6 back to CS4 you may download ONLY if you bought direct from Adobe via download
-Log-in to your account and click this link https://account.adobe.com/products
--click Order history on the left and then the link to your order that will show on the right
--and finally click the link "Downloads and serial numbers" that will appear
---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 have what you need
-if you did not buy direct from Adobe via download 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 disc Adobe does not provide a replacement via download
-if you bought a download from a 3rd party vendor you will need to contact that vendor

If that doesn't work do a search for a link at https://prodesigntools.com

There is one for version 6 https://prodesigntools.com/adobe-lightroom-6-cc-direct-download-links.html

I do NOT know if there is one for version 5