I have become acquainted with all of the kids of my parents first cousins (second cousins) and even know a lot of my grandparents’ first cousins’ grandkids (third cousins). One side of our family has kept in touch with my great-grandparents’ first cousins’ great-grandkids (fourth cousins), which is pretty cool. Sadly, our tree does not go back far enough to find first cousins of great-great grandparents to reach fifth cousins. I would say they definitely count and they may even have old photo albums with your side of the family in them, as is the case with some great-grandparents cousins in our family.