Photos was unable to open the library “Photos Library.photoslibrary”. (5416)

Which system update did you install? You may want to check, if your external drive is compatible with Photos. It will depend on the system version, if it can open a library at all, if the derive is not suitable. Some older system versions have been more tolerant and let you keep the library on volume, where the Photos Library might get damaged.

See: Move your Photos library to save space on your Mac - Apple Support

The most important things to check are:

• The file system format needs to be APFS or MacOS Extended (Journaled)
• The drive needs a wired connection, it must not be on a network share on your local network.
• The volume with the library should not have been used for Time Machine backups or have other backup software installed.
• If you cannot set the "Ignore ownership on this volume" flag for the external volume, there is a problem with your external drive.

If the external drive is not suitable, move your Photos Library to a different volume, where it is save to store the photos. Then try to repair the library: Repair your library in Photos on Mac - Apple Support (BH)