Row Numbering for every n-th multiple

Nice question! Unfortunately my editor is struggling with the Greek characters, so I hope you do not mind me using ASCII characters in the example. Of course, the code does work in your use case, too. You can use \numexpr to define a mod function by exploiting that it rounds fractions.

\documentclass[letterpaper,12pt]{article}

\usepackage{array}
\newcounter{rowcount}
\setcounter{rowcount}{0}

\begin{document}
\begin{tabular}{@{\stepcounter{rowcount}%
\ifnum\the\numexpr\value{rowcount}-5*(\value{rowcount}/5)=0\relax
\number\value{rowcount}%
\fi
\hspace*{\tabcolsep}
}lc}
 & A \\
 & B \\
 & C \\
 & D \\
 & E \\
 & F \\
 & G \\
 & H \\
 & I \\
 & J \\
 & K \\
 & L \\
 & M \\
 & N \\
 & O \\
 & P \\
 & Q \\
 & R \\
 & S \\
 & T \\
 & U \\
 & V \\
 & W \\
 & X \\
 & Y \\
 & Z \\
\end{tabular}
\end{document}

One can of course use a macro and condense it but I wanted to keep the trick explicit. It is also obvious (I hope;-) how to generalize this to other integers, i.e. not 5. You can define this to be a new column type.

\documentclass[letterpaper,12pt]{article}
\usepackage{array}
\newcounter{rowcount}
\setcounter{rowcount}{0}
\newcolumntype{N}[1]{@{\stepcounter{rowcount}%
\ifnum\the\numexpr\value{rowcount}-#1*(\value{rowcount}/#1)=0\relax
\number\value{rowcount}%
\fi
\hspace*{\tabcolsep}
}l}
\begin{document}
\begin{tabular}{N{4}c}
 & A \\
 & B \\
 & C \\
 & D \\
 & E \\
 & F \\
 & G \\
 & H \\
 & I \\
 & J \\
 & K \\
 & L \\
 & M \\
 & N \\
 & O \\
 & P \\
 & Q \\
 & R \\
 & S \\
 & T \\
 & U \\
 & V \\
 & W \\
 & X \\
 & Y \\
 & Z \\
\end{tabular}
\end{document}

Your idea is good. I defined a \countrows command that has as optional argument the interval of the numbering. Omitting it will number all lines.

I decided to set the numbers in the margin, with smaller type size, but this can be modified by changing the definition.

\documentclass[letterpaper,12pt]{article}
\usepackage{polyglossia}
\usepackage{fontspec}
\usepackage{array}

\setmainfont{Libertinus Serif}
\setmainlanguage[variant=us]{english}
\setotherlanguage[variant=ancient]{greek}

\ExplSyntaxOn
\int_new:N \g_robxxviii_rowcount_int

\NewDocumentCommand{\countrows}{O{1}}
 {
  \int_gincr:N \g_robxxviii_rowcount_int
  \int_compare:nT { \int_mod:nn { \g_robxxviii_rowcount_int } { #1 } = 0 }
   {
    \makebox[0pt][r]
     {
      \footnotesize
      \int_to_arabic:n { \g_robxxviii_rowcount_int }\hspace{\tabcolsep}
     }
   }
 }
\NewDocumentCommand{\resetcountrows}{}
 {
  \int_gzero:N \g_robxxviii_rowcount_int
 }
\ExplSyntaxOff

\begin{document}

\section*{Fragment I.1: Psalm 17:26b-(LXX)}

\begin{greek}
\noindent\resetcountrows
\begin{tabular}{
  @{\countrows[5]}
  ccccc
  >{\bfseries}r
  @{}
}
ουεμ     & καί μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & καὶ μ(ετ)α\\
γαβρ     & ἀν̣δρὸ̣ς̣         & ἀνδρὸ̣ς̣          & ἀνδρὸς     & ἀνδρὸς\\
θαμιμ    & τ(ε̣λ̣)ει̣ου̣      & ἀκέ̣ραιον        & ἀθώιου     & ἀμωμου\\
θεμαμ̣μ̣α̣μ̣ & τ(ελ)(ε̣ι̣)ωθήσι̣ & ἀκέραια π̣ρά̣ζεις & ἀθώος ἔσηι &  ἄμωμος (ἔσ)ηι\\
ουεμ     & καὶ μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & μ(ετ)α & 27\\ 
ναβαρ \\
ουεμ     & καί μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & καὶ μ(ετ)α\\
γαβρ     & ἀν̣δρὸ̣ς̣         & ἀνδρὸ̣ς̣          & ἀνδρὸς     & ἀνδρὸς\\
θαμιμ    & τ(ε̣λ̣)ει̣ου̣      & ἀκέ̣ραιον        & ἀθώιου     & ἀμωμου\\
θεμαμ̣μ̣α̣μ̣ & τ(ελ)(ε̣ι̣)ωθήσι̣ & ἀκέραια π̣ρά̣ζεις & ἀθώος ἔσηι &  ἄμωμος (ἔσ)ηι\\
ουεμ     & καὶ μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & μ(ετ)α & 27\\ 
ναβαρ \\
ουεμ     & καί μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & καὶ μ(ετ)α\\
γαβρ     & ἀν̣δρὸ̣ς̣         & ἀνδρὸ̣ς̣          & ἀνδρὸς     & ἀνδρὸς\\
θαμιμ    & τ(ε̣λ̣)ει̣ου̣      & ἀκέ̣ραιον        & ἀθώιου     & ἀμωμου\\
θεμαμ̣μ̣α̣μ̣ & τ(ελ)(ε̣ι̣)ωθήσι̣ & ἀκέραια π̣ρά̣ζεις & ἀθώος ἔσηι &  ἄμωμος (ἔσ)ηι\\
ουεμ     & καὶ μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & μ(ετ)α & 27\\ 
ναβαρ \\
ουεμ     & καί μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & καὶ μ(ετ)α\\
γαβρ     & ἀν̣δρὸ̣ς̣         & ἀνδρὸ̣ς̣          & ἀνδρὸς     & ἀνδρὸς\\
θαμιμ    & τ(ε̣λ̣)ει̣ου̣      & ἀκέ̣ραιον        & ἀθώιου     & ἀμωμου\\
θεμαμ̣μ̣α̣μ̣ & τ(ελ)(ε̣ι̣)ωθήσι̣ & ἀκέραια π̣ρά̣ζεις & ἀθώος ἔσηι &  ἄμωμος (ἔσ)ηι\\
ουεμ     & καὶ μ(ετ)α     & πρὸς            & καὶ μ(ετ)α & μ(ετ)α & 27\\ 
ναβαρ \\
\end{tabular}
\end{greek}

\end{document}