Jumping frame contents with beamer and pgfplots

This what the overlay-beamer-styles edit is for. In addition, I like the [t] option, which does not help here, but in general it helps avoiding jumps when working with \only. In addition I gave the y ticks a fixed width. (Your plot is a bit too wide.)

\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{overlay-beamer-styles}
\begin{document}

\begin{frame}[t]% <- I prefer [t] to avoid jumps 
    text

   \begin{center}
        \begin{tikzpicture}
            \pgfplotsset{scaled ticks=false,ytick style={text
            width=2cm,align=right},
                    ticklabel style={/pgf/number format/fixed,/pgf/number format/1000 sep={\,}},
                    width=11cm,
                    height=6cm}
            \begin{axis}[visible on=<1>]
                 \addplot [domain=0:5] {x^3}; 
            \end{axis}
            \begin{axis}[visible on=<2>]
                 \addplot [domain=0:15] {x^3}; 
            \end{axis}
            \begin{axis}[visible on=<3>]
                 \addplot [domain=0:100] {x^3}; 
            \end{axis}
            \begin{axis}[visible on=<4>]
                 \addplot [domain=0:1000] {x^3}; 
            \end{axis}

        \end{tikzpicture}
  \end{center}      
\end{frame}

\end{document}

This allows zooming out by fixing the axis size and the bounding box.

\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}

\begin{document}

\begin{frame}
    text

    \begin{center}
        \begin{tikzpicture}
            \path (-2.5cm,-1.5cm) (8.5cm,4.5cm);% bounding box
            \begin{axis}[
                    scaled ticks=false,
                    ticklabel style={/pgf/number format/fixed,/pgf/number format/1000 sep={\,}},
                    width=8cm,
                    height=4cm,
                    scale only axis,
                    %enlargelimits=false% not needed after all
                ]
                \only<1>{ \addplot [domain=0:5] {x^3}; }
                \only<2>{ \addplot [domain=0:15] {x^3}; }
                \only<3>{ \addplot [domain=0:100] {x^3}; }
                \only<4>{ \addplot [domain=0:1000] {x^3}; }
            \end{axis}
        \end{tikzpicture}
    \end{center}
\end{frame}

\end{document}