4th - 6th cousin level may be closer than you think because it is not taking into account generations removed
Exactly the situation in my tree. I've had a mystery 2nd-3rd cousin match ever since my test results came back, the match has no tree, no profile information, nothing to indicate where/when they were born and hasn't responded to messages. The name is too common to make any assumptions.
A new match came up last week marked as a 4th-6th cousin, like most at that sort of level it's easy to overlook as being worthy of much investigation but as a shared match to the mystery match I decided to dig a little deeper. The new match is only 18 years old and is the grandchild of my mystery match. I'm glad I did follow up as the 18yo is much closer than the headline 4th-6th cousin suggestion. The real work is still ahead of us as it's linked to an NPE in my tree and potentially could blow their well documented tree apart too but it would have been so easy to miss what could be a very important match as the suggested relationships can be very misleading.