I have many Family Finder matches in the “4th – remote cousin” and “5th – remote cousin” ranges. I cannot find the connection. Are these false positives?

These matches are in the Speculative Relationship category. Their quality should be taken as exactly that. Your relationship may be as close as 4^th cousins. On the other hand, you may share some autosomal DNA with cousins beyond genealogical times. Thus, it may also be as remote as 20^th cousins. It is not possible to say exactly where the relationship falls.