Transferring Photos library Ver 5.0 to external drive

Yes this can be done, and easily. Simply hold the option key when launching Photos and select the library on the external to open.

But remember that external needs to be formatted Mac OS X Extended, Journaled or apfs, otherwise your library is liable to silent corruption and dataloss.

This message

and tells me I need Photos 9.

means that the library has been updated to the v9 format, and older versions won't open it. This happens when you open the library with version 9 of Photos.

Do you have a backup copy of your Photos Library from the time before you opened it in Photos 9 on Sonoma? Perhaps in your Time Machine backup?

Then restore this version to your external drive, but do not overwrite the Version 9 version. Each of your Macs will need a different version of the Photos Library.

As Yer_Man said, when a Photos Library is opened by a newer Operating System, it is updated to accommodate that system. The database gets new columns to allow for the new features, and so a Photos Library can not be opened in an older OS. There's just no way for that older version to read the new stuff in the revised version.

The only way to use a Photos Library with two different OSs is to connect to iCloud Photos. When you turn on iCloud for Photos, copies of the pictures get uploaded to iCloud. Then other devices, even with other OSs, can download the parts they want and work normally. You can also, if storage is limited, have Photos download smaller versions of the pictures to save space. It will then go to iCloud to get the full sized image whenever you want to edit or zoom or print or whatever needs the full resolution.