DNA Match between Fourth and Fifth Cousins

I met a fifth cousin online ("R.B.") when she wrote to me after I posted pictures of our mutual family graves.  Our common ancestors are our 4th great grandparents, Stephen Cook (1797-1853) and Elizabeth vanderHoof (1799-1878) of Morris County, New Jersey.  R.B. tested her autosomal DNA at FamilyTreeDNA while most of my family tested at 23andMe.  I previously uploaded results for some family members from 23andMe to FamilyTreeDNA, but R.B. was not in the matches.  Once you reach the third cousin level, your chances of sharing any identical autosomal DNA drop.

So we turned to GedMatch to compare our DNA.  GedMatch accepts files of DNA tests done at Ancestry, 23andMe, and FamilyTreeDNA.

R.B. and I share no detectable identical DNA.

GedMatch.com
No DNA detected between my fifth cousin, R. B., and me

Fortunately, I have members of the prior generation to test.  When choosing relatives to take DNA tests, the oldest generation available is preferred because half the DNA is lost with each new generation.

R.B. shares a little identical DNA with my father and my father's third cousin from this Cook line.  This could be a coincidence of no genealogical value, or it could be the same DNA passed generation to generation from Stephen Cook or Elizabeth vanderHoof.

GedMatch.com
Autosomal DNA comparison between 4th cousins, once removed
The segment size (11.1 cM) is good, but the number of SNPs (1038) may be too low to be identical by descent.
A relationship was predicted within six generations, which is fairly accurate.

GedMatch.com
Autosomal DNA comparison between 4th cousins, once removed
Both the segment size (6.6 cM) and the number of SNPs (1017) may be too low to be identical by descent.
No predicted relationship.

Fortunately, my father's siblings have also tested.  One sibling may demonstrate a match where another one will not.  That is the case with my uncle.

GedMatch.com
Autosomal DNA comparison between 4th cousins, once removed
Two identical segments of DNA are found.  Both brothers share the segment on chromosome 15 with R.B.
The segment on chromosome 3 contains more SNPs and is more likely to indicate a shared ancestor. 

R.B. and my uncle share two small segments of identical DNA, enough to trigger an estimate to the Most Recent Common Ancestor:  4.7 generations.  The actual number of generations back to the most common recent ancestors, Stephen Cook and Elizabeth vanderHoof, is 5 generations from my father and uncle and 6 generations from R.B.

Chart of Consanguinity
My uncle is 5 generations from Stephen Cook and Elizabeth vanderHoof,
while R.B. is 6 generations from this couple,
so R.B. and my uncle are 4th cousins, once removed.

What is gained from this information?  Two items.
First, the shared DNA within the parameters of the 4th to 5th cousin range makes it more likely that we have the correct Cook family lines.  It is not proof that we are related through Cook and vanderHoof, as the identical DNA could be from another shared line that we are unaware of at this time.
Second, we can view other genetic cousin matches on these same segments and specifically look for connections to Cook or vanderHoof.