How to draw a large arrow with text between two tikz pictures?

As you have defined it, this arrow is a TikZ node. It is therefore useless to create a LaTeX command to draw it, just use the style My Arrow Style you have created.

To place it, with the positioning library, I placed it on the right of the north anchor of the node (2)

node[My Arrow Style,right=of 2.north]{some text};

documentclass[standalone]{beamer}
usepackage{tikz}
usetikzlibrary{arrows.meta, shadows, fadings,shapes.arrows,positioning}
tikzset{My Arrow Style/.style={single arrow, fill=red!50, anchor=base, align=center,text width=2.8cm}}
%newcommand{MyArrow}[2][]{tikz[baseline] node [My Arrow Style,#1] {#2};}

begin{document}
begin{frame}
    begin{center}
    begin{tikzpicture}[scale=0.6]
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (1) at (0, 0) {1};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (2) at (2, -2) {2};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (3) at (4, -4) {3};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (4) at (6, -6) {4};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (5) at (8, -8) {5};
    path (1) edge [loop above] node {} (1);
    path (2) edge [->] node {} (1);
    path (3) edge [->] node {} (2);
    path (4) edge [->] node {} (3);
    path (5) edge [->] node {} (4);
    node[My Arrow Style,right=of 2.north]{some text};
    begin{scope}[shift={(13cm, -1cm)}]
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (1) at (0,0) {1};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (2) at (-2, -2) {2};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (3) at (0,-2) {3};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (4) at (2, -2) {4};
    node[shape=circle,draw=black,fill=white, drop shadow,minimum size=1cm] (5) at (4, -2) {5};

    path (1) edge [loop above] node {} (1);
    path (2) edge [->] node {} (1);
    path (3) edge [->] node {} (1);
    path (4) edge [->] node {} (1);
    path (5) edge [->] node {} (1);
    end{scope}
    end{tikzpicture}
end{center}
end{frame}
end{document}