When you started Cubase 10.5 for the very first time, all the preferences of Cubase 10.0 should migrate to Cubase 10.5. It seems this didn’t happened otherwise you would get exactly the same settings, you had in Cubase 10.0 and the list of Recently opened files would be available too.
So you could try to trash Cubase 10.5 preferences and start Cubase 10.5 again. Hopefully the preferences would migrate now.
If this wouldn’t work, you can use Profile Manager to migrate the settings manually. But I’m afraid, recent projects are not part of the Profile (actually it doesn’t make much sense).
The .cpr files themselves don’t belong to one version of Cubase or another. Cubase like almost every other Windows Program does maintain a list of recently opened files. But C10 and C10.5 are different programs and their lists will naturally differ because each program has opened different Projects in different orders. Indeed when C10.5 (or any Windows Program) is first installed its list will be empty because it hasn’t opened any Projects yet.
Double clicking on a Project file should open it in C10.5, and add it to that program’s recent file list.
If double-clicking opens C10 instead, that means that Windows is still associating the .cpr file type with C10 and not C10.5. Right click on the Project file and use “Open With” to change the Windows file association.
Are you sure about this? I mean, there is one exception, I would say.
The recent projects list is part of Cubase Preferences files. So when you are using C10 so you make the recent file list and then you upgrade to C10.5 and your preferences are migrated from C10 to C10.5 (during the very first C10.5 start), the list of the recent files (of C10) should appear in C10.5 too (as far as I know).
Then, of course, the preferences of C10 and C10.5 are handled independently, so even the lists of recent files are handled independently in both Cubase versions.
I stand corrected after checking. Internal to Cubase the list does migrate along with the other Preferences (or should at least). The list that Windows itself maintains is empty immediately after installation & then gets populated.
You don’t have to redo the upgrade. Just delete Cubase 10.5 preferences and start Cubase 10.5 again. Cubase 10 preferences should be migrated over to Cubase 10.5.
Please, make sure, your Cubase 10 is installed in the default path (i.e. at the system C drive).