You probably can, but I'd be very cautious. Please keep in mind that unlike other sites where you record you genealogy is isolation, FamilySearch is more like "the tree of all mankind". People are expected to work collaboratively as you no doubt have lots of distant cousins also working on the same lines.
Once you get above the Grandparent to Great-grandparent level, there's very good odds they're already there. If you import 5600 name, I'd wager that you'd create over 5,000 duplicate individuals. What's more, you'd probably want to associate source material with the names you add to back up the assertions being made. As someone once said "Genealogy without sources are fairytales".
I think you'll find in this system, the work is far, far easier than it was even 10 years ago.
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