Use this
\begin{tikzpicture}
\def \n {5}
\def \radius {3cm}
\def \margin {8} % margin in angles, depends on the radius
\foreach \s in {1,...,\n}
{
\node[draw, circle] at ({360/\n * (\s - 1)}:\radius) {$\s$};
\draw[->, >=latex] ({360/\n * (\s - 1)+\margin}:\radius)
arc ({360/\n * (\s - 1)+\margin}:{360/\n * (\s)-\margin}:\radius);
}
\end{tikzpicture}
to get
\begin{tikzpicture}
\def \n {5}
\def \radius {3cm}
\def \margin {8} % margin in angles, depends on the radius
\foreach \s in {1,...,\n}
{
\node[draw, circle] at ({360/\n * (\s - 1)}:\radius) {$\s$};
\draw[->, >=latex] ({360/\n * (\s - 1)+\margin}:\radius)
arc ({360/\n * (\s - 1)+\margin}:{360/\n * (\s)-\margin}:\radius);
}
\end{tikzpicture}