I think Apple have been putting out warnings for quite a while regarding older software in relation to Catalina. So you can never uninstall or re-install. Some customers have found that they still have some functionality if the app was already installed at the time of the upgrade to Catalina but I don’t think it will ever be perfect. You could try adding LR5 to the control list:
Open System Preferences
Go to Security & Privacy
Open the Accessibility tab
Click the lock and enter your Apple password
Look for Lightroom 5 and the message “Allow the apps below to control your computer” or click Add.
You should not allow Lightroom to control the computer (there's no harm in that, but it won't solve your problem), but you should give Lightroom permissions to access certain folders. Either check the options as in this screenshot, or even easier: Add Lightroom to 'Full Disk Access' above that.