I'm in the process of researching upgrading our Enterprise Geodatabase. Historically, our current 10.7.1 geodatabase wasn't well maintained, so we are looking at taking a start from scratch approach instead of cleaning up and upgrading our currently EGDB.
That being said, we are currently on Enterprise 11.4, with hopes to upgrade to 11.5 in the fall/winter season. Is it possible to run 11.4 on an 11.5 EGDB, if i just create a new EGDB through Pro 3.5/EGDB 11.5? Or would it be best practice to create the EGDB with match the current Enterprise/ArcGIS Server Clients that we are running?
It is recommended by Esri here that your EGDB and your ArcGIS clients (Pro, Server, etc.) all be at the same version. With that being said, it isn't a requirement.
However, if you're going to mix and match versions, I'd recommend your EGDB be at the lowest version of the various software you're running. So in your case, it would be a 11.4 EGDB since you're running Enterprise 11.4 (even though you're running Pro 3.5). That will ensure that your EGDB is fully supported by all your ArcGIS clients.
Generally, I believe an 11.5 EGDB will work with Enterprise 11.5, but any new EGDB functionality released in 11.5 might not be compatible with Enterprise 11.4. But like I said, it's recommended that you keep your EGDB and all ArcGIS clients at the same version.