There are some issues with Lightroom running on MacOS 12.12
I wan't to update my version to Lightroom 6.x Do I have to install first 5.7 and then run the update file?
Install Lightroom 6. Then update to Lightroom 6.7. No need to worry about any version of Lightroom 5.
Lightroom 6 is a new and completely different version from 5. It is a Paid upgrade and not an Update.
So you can buy LR 6 and update it to 6.7. Or you can subscribe to the Adobe Photographers plan and get both LR and PS for $10- a month.
If you already own LR 5 you can buy the LR 6 upgrade and there is no need to first install LR 5 before you install LR 6.