Hi Rob,
I have the CC Photo subscription. This is installed on my desktop computer and on my notebook. However, I still need a Lightroom installation on another notebook on which I manage completely different images. My previous second notebook, on which Lightroom 6 was installed, was defective. I now had to buy a new notebook.
I bought LR 5 on CD years ago and have the serial number. I also bought Lightroom 6, but I only have a Lightroom_6_LS11.exe file. This appears to be an update. The serial number for version 5 is also still available.
Lightroom 5 and 6 were installed as standalone versions. I can no longer access Lightroom 6 with its serial number because the app won't start.
I think your grandma is right and I can forget LR 6.
My attempt to install LR 5 from CD with serial number worked, but after that the program blocks.
I had already written the following about this:
"After starting, a window now always appears prompting me to update, but blocks the whole computer. LR 5 can only be closed via the Task Manager. I have also not found a process in the Task Manager that closes this window."
I am attaching the screenshot again.
If this window no longer appeared, I could work with Lightroom 5.
I would be so glad in case the installation works.
What computer Operating System? Lr5 & Lr6 cannot be installed or run on recent Mac OS, or even Windows-11 is doubtful. Maybe you OS is incopatible with legacy versions of Lr.
For Lr5 An upgrade to v5.7 is NOT available from Adobe, so you IGNORE that message (your screenclip).

You can download the complete Windows install file for v5.7.1 at- Lightroom 5 for Windows (957 MB) . SImply Install the downloaded file. You do not need your CD.! A registration number for v5.0 will work with v5.7.1
"I have the CC Photo subscription."- Please give more details. Do you pay a subscription fee for a Photography Plan? What plan do you see at- https://account.adobe.com/
If you have a subscription- What Apps do you see in your Adobe Creative Cloud Desktop App that you can install? Have you installed the Desktop App?

"Lightroom 6 with its serial number because the app won't start."- What happens when you try? Do you get any error messages? Do you see a startup Splash Screen? At install were you asked to enter both the Lr5 AND the Lr6 Serial numbers?
Lr6 will not start if you have Creative Cloud Desktop App installed and you don't pay a subscription.
Sorry I cannot be more helpful.