\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage[nomessages]{fp}
\usepackage{tikz}
\usetikzlibrary[topaths]
\begin{document}
\newcommand\n{5}
\begin{tikzpicture}
\foreach \number in {1,...,\n}{
\node[vertex] (N-\number) at ({\number*(360/\n)}:5.4cm) {};
}
\foreach \number in {1,...,\n}{
\foreach \y in {1,...,\n}{
\draw (N-\number) -- (N-\y);
}
}
\node[vertex,red] (N-3) at ({3*(360/\n)}:5.4cm) {};
\node[vertex,red] (N-5) at ({5*(360/\n)}:5.4cm) {};
\draw[green, ultra thick] (N-3) -- (N-5);
\end{tikzpicture}
\end{document}