This is the situation as we (other users like you- in this forum) know about v5.xx
-Adobe does not support v5 (Perpetual) in any way.
-Download (inc. upgrade to v5.7) is only avbailable from a trusted Third-party 'ProDesgnTools'
https://prodesigntools.com/lightroom-5-ddl-comparison-vs-lr4.html
-v5.xx will install in Windows-10.
-You would need the v5 Registration Serial Number.
-You do not need to install the Creative Cloud Desktop App (or any Cloud apps) to install v5.xx
-Save a copy of the .exe. install file after you download.
I think you have had a fairly good run of v5 since it was released in 2013 (8 years?) Don't you think it is about time to reward Adobe for their intellectual property with an upgrade to Version-11 (by subscription).
You "paid for" a licence to use their software (for 8 years!), it does not mean you have the software forever.
Many (millions?) of happy users have no "frustration" using Adobe Apps that are frequently upgraded for a meagre cost of subscribing.
$9.99 PHOTOGRAPHY PLAN (USA)
Regards. My System: Lightroom-Classic 14.0, Photoshop 26.0, ACR 17.0, Lightroom 8.0, Lr-iOS 9.0.1, Bridge 15.0.0, Windows-11.