The more distant the relationship, the less DNA you share.
You share 50% of your DNA from each parent - but that 50% is not necessarily shared exactly in half with your grandparents, so there is some variance in DNA shared, even for for a first cousin, which would still be a fairly high match - high enough to be able to be more exact. To back that up, I share 28%, 26%, 24% and 22% with each of my grandparents for example.
A first cousin's range would share around 12.5% which is around 850cM. There are a few relationships that would share a similar percentage. The average shared amount is 869cM.
A second cousin would share around 3.125% (around 212.5cM).
A third cousin, 0.718% (around 53cM).
A fourth cousin, 0.195% (around 14cM).
A fifth cousin, ~0.05%
As you can see, that is already a small percentage and as DNA is randomly inherited, the percentage difference becomes too tricky to decipher. This is why it will say 5th to 8th cousin.
There's a chance you could have a more distant relative in that zone or even a closer, it just depends on the random parts of DNA inherited by the 2 people matching and every ancestor up to the most common recent ancestor(s) they share.
