Anything above 5 and my OCD/anxiety sets in.
For working from home, since I don't have a second monitor handy, I tend to push that number occasionally (maybe 11 or 12 at most) but even then, I try to open a second browser window or whatever.
One of my co-workers showed me their set up, which was like.. 30+ tabs. They had a system and knew exactly where each tab was, but just looking at that gave me anxiety.