As I understand it, your closest matches in 5th to 8th cousin range are perhaps likely to be definitely connected to you, and with full trees on both sides, you might be able to confirm the match.
The further down the list you go, the less likely it is to be a) a genuine match and/or b) a confirmable match. If you click through to your last few pages, you are likely to share as little as 6cM with them. This can sometimes mean a false positive match, sometimes a very distant match. 5th to 8th cousins indicates possible 4G to 7G grandparents, and perhaps a generation or so before that. I haven't traced all of my 7G and 8G grandparents - I've got further back than that on a few lines, not so far on a few more. Add in the likelihood of your match knowing all of their 7G and 8G grandparents as fairly remote, if they even have an online tree.
You may strike lucky and you both have the same surname from the same small village. You may be unlucky - where you match could be the one great grandparent of some degree that you haven't been able to trace, or one of the 512 7G grandparents of some degree that your match has been unable to trace, or any other combination.
Or the match could be coincidental, IBS rather than IBD.
The lowest confirmed match I have found is of 6.7 cM with a 4th cousin twice removed. Many more follow her, as I said before down to 6 cM.
You just have to work away at them, bit by bit.
Regards Margaret