Can Y DNA I-CTS5966 and R-L51 be related

Are they all direct paternal links? No maternal relationship?
Seems unlikely since the time estimate for that paternal haplogroup branch is something like 53,000 years ago.

Yes all 4 of them are paternal links only

The 5thGGR had 2 sons, and then the those sons had like 6 sons each, and so on.

My father is a R-L51, Could we be related? Prior to getting this designation he was R-M269 I believe.

maybe where is your DNA test at? I have it on 23andMe, FamilyTreeDNA and Gedmatch. I think here too,

I am a R-L51 on 23andME , and ftDNA has me as a R-M269. I show a fourth cousin on 23andMe that shows a paternal Haplogroup of R-CTS4188.

My first cousin (my mother's brother's son) is R-L51 on 23andme, ftDNA has him as R-M269, is on gedmatch. His paternal surname and my maternal surname is "Foster". My gedmatch kit # is M694349. My cousin's ftDNA shows him as "unmatched" to the others on the Foster ydna project. Could he have been adopted?

Cynthia Flores, My Father's brother Rex Donald Baker has a Haplogroup R-L51. We are probably related. My Grandfather was Gerald William Baker and his father was William Lewis Baker Sr. Crystal Sherman

My Father Wm S Henderson tested R-M269, It was the further snp testing that the R-L51 designation came back. So R-L51 is more specific.