can't open photo library

Where is your Photos Library stored? Is it in your Pictures folder or are you keeping it on an external drive?

If the library is on an external drive, check, if the external drive is compatible with Photos 5 on Catalina.

Photos 5 cannot open and upgrade the library, if it is on volume, that has been used for Time Machine backups, or if the volume is remotely mounted, not directly plugged in, or if the file system format is not MacOS Extended (Journaled) or APFS. Move your Photos library to save space on your Mac - Apple Support

Is it the application which will not open or the library?

If you hold down the option key whilst opening Photos it will allow you to create a new library and then you can determine if the old library is corrupted or the application not opening correctly.

Alternatively, hold down option and command when opening the library and Photos will repair it.

When was the last time the library opened correctly, do you have a back-up version available?