If your detour is only a single page, you could jump back to the previous view using your pdf viewer. For example in adobe reader, the keyboard shortcut is `cmd+left arrow` (mac) or `alt+left arrow` (other operating systems). Most pdf viewers will have a shortcut, check their documentation to see what they use.

----

If you give your 5th frame a label, say `foo`, you can add a link to it in your first frame with `\hyperlink{foo}{return to frame 5}`:

```
\documentclass[xcolor=dvipsnames]{beamer}

\definecolor{myblue}{rgb}{0.00,0.00,0.50}
\setbeamercolor{title}{bg=myblue!80!white}
\setbeamerfont{frametitle}{series=\mdseries}

\usecolortheme[named=myblue]{structure}
\usefonttheme[onlymath]{serif} % rendre l'ecriture math plus beau (perhaps no necessary)
%%%%%%%%%%%%%%%%%%%%%%%%%\usepackage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-----pour faire diagramm-------------
\usepackage{tikz-cd}
\usetikzlibrary{overlay-beamer-styles}
%---------------------------
\usepackage{pifont} %bouni
\usepackage{tabularx}
%%%%%%%%%%%%bclogo%%%%%%%%%%%
\usepackage{soul}
\setul{}{1.5pt}
\usepackage[tikz]{bclogo}
\colorlet{bctitle}{Maroon}
\renewcommand\bcStyleTitre[1]{\vskip-0.8em\bfseries\color{bctitle}\ul{#1}\vskip-0.7em}
%%%%%%%%%%%%%%%%%%%%%%%
%-----
\usepackage{fancybox} %pour faire l'encadrement
\newcommand{\cadre}[1]{
\setlength{\fboxsep}{7pt}
\begin{center}
\shadowbox{#1}
\end{center}}
%-----encadrer equations--------------
\usepackage{empheq}
\definecolor{shadowcolor}{RGB}{0, 0, 102}
\newcommand*\eqbox[1]{%
  \setlength\shadowsize{2pt}%
  \shadowbox*{#1}%
}
%%%%%%%%%%%%%%%%%%%%%%%

%----------pabox----------
\usepackage[most]{tcolorbox}

\newtcolorbox{mybox}[2][]{%
    colback=bg,
    colframe=blue!75!black,
    fonttitle=\bfseries,
    coltitle=blue!75!black,
    colbacktitle=bg,
    enhanced,
    attach boxed title to top left={yshift=-1.2mm, xshift=2mm},
  title=#2,
  #1}
%--------------------
%------------------------\AtBeginSubsection[]----------------------
    \AtBeginSubsection[]{   
        \begin{frame}<beamer>[noframenumbering,plain]{Plan of the talk} %Outline
            \transsplitverticalout
            \tableofcontents[currentsection,currentsubsection]
        \end{frame}
    }

%-------------------------------------------------------

    \usetheme{Madrid}
    \useoutertheme{shadow}

    %-----------------custom frame title background--------------------
    \makeatletter
    \pgfdeclarehorizontalshading[titleleft,titleright]
    {beamer@frametitleshade}
    {\paperheight}{%
    color(0pt)=(titleleft);
    color(\paperwidth)=(titleright)}
    \makeatother
%%%%% Custom color definitions used in the head and foot line of the frames %%%%%
\colorlet{newblue}{blue!30!black} %<----- define the new color myblue (newblue or myblue)
%\colorlet{myyellow}{yellow!30!white} %<----- define the new color myyellow
\definecolor{myyellow}{RGB}{240,230,140}

    \setbeamercolor{author in head/foot}{bg=newblue} %<----- background color of author in footline
    \setbeamercolor{title in head/foot}{bg=myyellow,fg=newblue} %<----- background color and font color for presentation title in footline
    \setbeamercolor{page number in head/foot}{bg=newblue,fg=white} %<----- background and font color foot page numbers in the footline

    \setbeamercolor*{section in head/foot}{bg=newblue, fg=white} %<----- background and font color for the sections in the header
    \setbeamercolor*{subsection in head/foot}{bg=myyellow,fg=newblue} %<----- background and font color for the subsections in the header

%\definecolor{new}{RGB}{102,102,0} gray
    \colorlet{titleleft}{newblue}  %<----- left half of frame title background color
    \colorlet{titleright}{newblue} %<----- right half of frame title background color
    \setbeamercolor*{frametitle}{fg=white} %<---- Color of the frame title text  white
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%------begin Warsaw----------------------------------
%\usetheme{Warsaw}
\setbeamertemplate{headline}{} % supprimer le headline-il faut ici
%------
%-----------------------------footline-----------------------------
    \setbeamertemplate{footline}{
        \leavevmode%
        \hbox{%
            \begin{beamercolorbox}[wd=.11\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
                \usebeamerfont{author in head/foot}\insertshortauthor
            \end{beamercolorbox}%
            \begin{beamercolorbox}[wd=.81\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
                \usebeamerfont{title in head/foot}\insertshorttitle
    %            \hspace*{3em}
    %            \insertframenumber{} / \inserttotalframenumber\hspace*{1ex}
            \end{beamercolorbox}%
            \begin{beamercolorbox}[wd=.08\paperwidth,ht=2.25ex,dp=1ex,center]{page number in head/foot}%
    %            \usebeamerfont{title in head/foot}\insertshorttitle\hspace*{3em}
                \insertframenumber{} / \inserttotalframenumber
            \end{beamercolorbox}%
        }%
        \vskip0pt%
    }
%%------------------%%%%%%%%%%%%%%%%%%
\makeatletter
\AtBeginSection[%
    % version for sections without numbers
    {
        \begin{frame}[noframenumbering,plain]
            \centering
        \begin{minipage}{.8\textwidth}
                \begin{beamercolorbox}[colsep=-4bp,rounded=true,shadow=\beamer@themerounded@shadow,sep=8pt,center]{title}
                    \usebeamerfont{title}
                    \insertsectionhead
                \end{beamercolorbox}
        \end{minipage}
            \transboxout
        \end{frame}
    }
]{%
    % versions for sections with numbers
    \begin{frame}[noframenumbering,plain]
        \centering
        \begin{minipage}{.4\textwidth}
            \centering\color{myblue}
            \hrule width \hsize height 1pt  \kern 1pt \hrule width \hsize height 1pt \vskip5pt
            
            \Large\bfseries
            PART - \thesection\ -
            
            \vskip5pt \hrule width \hsize height 1pt  \kern 1pt \hrule width \hsize height 1pt
        \end{minipage}

        \vspace{1cm}

    \begin{minipage}{.8\textwidth}
            \begin{beamercolorbox}[colsep=-4bp,rounded=true,shadow=\beamer@themerounded@shadow,sep=8pt,center]{title}
                \usebeamerfont{title}
                \insertsectionhead
            \end{beamercolorbox}
    \end{minipage}
        \transboxout
    \end{frame}
}
\makeatother
%%%%%%%%%%%%%%%perhaps non necessary%%%%%%%%%%%%%%%%%%%%%
%-----accent                        
%\usepackage[utf8]{inputenc} %ecrire directement les accents et il peut poser des probleme
\usepackage[T1]{fontenc}
%-----
%\usepackage{amsmath,amssymb,amsfonts} %math
\usepackage{empheq, nccmath} % empheq package loads mathtools
\usepackage{amssymb, amsthm, mathrsfs}
%---------------------------------------------
\setbeamertemplate{navigation symbols}{} % supprimer trace de la sourie
%\setbeamertemplate{headline}{} % supprimer le headline

%%%%%%newcommand%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%lemma%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%------------------------------------------------
\definecolor{kkgray}{RGB}{138,43,226}

\BeforeBeginEnvironment{lemma}{%
    \setbeamercolor{block title}{fg=white,bg=kkgray}
    \setbeamercolor{block body}{fg=black, bg=kkgray!20!white}
}
%------pour que le nom des auteurs soient entre [.......]
\setbeamertemplate{theorem begin}{%
       \begin{\inserttheoremblockenv}
       {%
         \inserttheoremname
         \ifx\inserttheoremaddition\@empty\else\ \hfill[\inserttheoremaddition]\fi%
       }%
     }
%------
\AfterEndEnvironment{lemma}{
        \setbeamercolor{block title}{use=structure,fg=white,bg=structure.fg!75!black}
        \setbeamercolor{block body}{parent=normal text,use=block title,bg=block title.bg!10!bg}
}
%------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%definition%%%%%%%%%%%%%%%%{RGB}{124,71,50}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%{rgb}{0.58, 0.77, 0.45}
\makeatletter
\definecolor{kaisbrown}{RGB}{210,105,30}

     \BeforeBeginEnvironment{definition}{%
   \setbeamercolor{block title}{fg=white,bg=kaisbrown}
     \setbeamercolor{block body}{fg=black, bg=kaisbrown!20!white}
     \setbeamertemplate{theorem begin}{%
       \begin{\inserttheoremblockenv}
       {%
         \inserttheoremname
         \ifx\inserttheoremaddition\@empty\else\ \hfill[\inserttheoremaddition]\fi%
       }%
     }
      }
    \AfterEndEnvironment{definition}{
    \setbeamercolor{block title}{use=structure,fg=white,bg=structure.fg!75!black}
    \setbeamercolor{block body}{parent=normal text,use=block title,bg=block title.bg!10!bg}
    \setbeamertemplate{theorem begin}[default]
        }
 %------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%proposition%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
 \newtheorem{proposition}[theorem]{Proposition}
  \definecolor{kaiscyan}{RGB}{0,139,139}  %72,61,139

     \BeforeBeginEnvironment{proposition}{%
   \setbeamercolor{block title}{fg=white,bg=kaiscyan}
     \setbeamercolor{block body}{fg=black, bg=kaiscyan!20!white}
     \setbeamertemplate{theorem begin}{%
       \begin{\inserttheoremblockenv}
       {%
         \inserttheoremname
         \ifx\inserttheoremaddition\@empty\else\ \hfill[\inserttheoremaddition]\fi%
       }%
     }
      }
    \AfterEndEnvironment{proposition}{
    \setbeamercolor{block title}{use=structure,fg=white,bg=structure.fg!75!black}
    \setbeamercolor{block body}{parent=normal text,use=block title,bg=block title.bg!10!bg}
    \setbeamertemplate{theorem begin}[default]
        }
 %------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%theorem%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\definecolor{kaispurple}{RGB}{128,128,0}  %147,112,219
    \BeforeBeginEnvironment{theorem}{%
   \setbeamercolor{block title}{fg=white,bg=kaispurple}
     \setbeamercolor{block body}{fg=black, bg=kaispurple!20!white}
     \setbeamertemplate{theorem begin}{%
       \begin{\inserttheoremblockenv}
       {%
         \inserttheoremname
         \ifx\inserttheoremaddition\@empty\else\ [\inserttheoremaddition]\fi%
       }%\hfill
     }
      }
    \AfterEndEnvironment{theorem}{
    \setbeamercolor{block title}{use=structure,fg=white,bg=structure.fg!75!black}
    \setbeamercolor{block body}{parent=normal text,use=block title,bg=block title.bg!10!bg}
    \setbeamertemplate{theorem begin}[default]
        }
%%%%%%%%%%%%%%%%%%%%%%-------------------------------------------------
\usepackage[usestackEOL]{stackengine}
%----------
%\setbeamertemplate{itemize items}{\ding{228}}

%%%%%%%%%%%%%%%%%%%%%%\begin{document}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}
\begin{theorem}[\ding{43} Author (2022)]
Let $\mathbb{T}= (T_{ij})_{d \times d}\in \mathbb{B}(\mathbb{H}^d)$ be such that $T_{ij}\in \mathbb{B}_{A^{1/2}}(\mathcal{H})$ for all $i,j\in\{1,\ldots,d\}$ and $\widehat{\mathbb{T}}^{\mathbb{A}}=(\|T_{ij} \|_A)_{d\times d}$. Then, $r_{\mathbb{A}}(\mathbb{T})\leq r(\widehat{\mathbb{T}}^{\mathbb{A}}).$ That is
\begin{equation*}\label{kk2020}
r_{\mathbb{A}}\left[ \begin{pmatrix}
T_{11}  &\ldots& T_{1d}\\
T_{21} &\ldots& T_{2d}\\
\vdots  & \vdots & \vdots\\
T_{d1}  &\ldots& T_{dd}
\end{pmatrix}\right] \leq
r \left[\begin{pmatrix}
\|T_{11}\|_A  &\ldots& \|T_{1d}\|_A\\
\|T_{21}\|_A  &\ldots& \|T_{2d}\|_A\\
\vdots &  \vdots & \vdots\\
\|T_{d1}\|_A  &\ldots& \|T_{dd}\|_A
\end{pmatrix} \right].
\end{equation*}
\end{theorem}
\pause
\begin{theorem}[\ding{43} Author (2022)]
Let $T_1,T_2,S_1,S_2\in \mathbb{B}_{A^{1/2}}(\mathcal{H})$. Then,
\begin{align}\label{eq1}
r_A\left(T_1S_1+T_2S_2\right)
& \leq \frac{1}{2}\sqrt{\left(\left\| S_1T_1\right\|_A -\left\| S_2T_2\right\|_A \right)
^{2}+4\left\| S_1T_2\right\|_A \left\| S_2T_1\right\|_A}\nonumber\\
&\quad \quad\quad \quad+\frac{1}{2}\Big( \left\| S_1T_1\right\|_A +\left\| S_2T_2\right\|_A%
\Big).
\end{align}%
\end{theorem}
\hyperlink{foo}{return to frame 5}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[label=foo]{}
\begin{theorem}[\ding{43} Author (2022)]
Let $T_1,T_2,S_1,S_2\in \mathbb{B}_{A^{1/2}}(\mathcal{H})$. Then,
\begin{align}\label{eq2}
r_A\left(T_1S_1+T_2S_2\right)
& \leq\frac{1}{2} \sqrt{\Big( \omega_A(S_1T_1) -\omega_A(S_2T_2)\Big)
^{2}+4\left\| S_1T_2\right\|_A \left\| S_2T_1\right\|_A }\nonumber\\
&\quad\quad\quad\quad+\frac{1}{2}\Big(\omega_A(S_1T_1) +\omega_A(S_2T_2)\Big).
\end{align}%
Moreover, the inequality \eqref{eq2} refines \eqref{eq1}.
\end{theorem}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document} 
```