How to overlap two adjacent edges of 2 framed minipages placed side by side?

Question

How to overlap the adjacent edges? In other words, the adjacent edges should be combined into one edge shared between to minipages such that all rules will have the same thickness.

\documentclass[10pt,dvipsnames,dvips,cmyk]{article}
\usepackage[a5paper,margin=10mm,showframe]{geometry}
\usepackage{lipsum,calc,xcolor}
\setlength{\fboxrule}{2mm}
\setlength{\fboxsep}{2mm}
\begin{document}\noindent{\color{red}%
\fbox{%
\begin{minipage}{0.5\textwidth-2\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}%
\fbox{%
\begin{minipage}{0.5\textwidth-2\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}}
\end{document}

---

EDIT 1:

Assume using table is prohibited by the game rule.

Answer 1

\documentclass{article}
\usepackage[a5paper,margin=10mm,showframe]{geometry}
\usepackage{lipsum,calc,xcolor}
\setlength{\fboxrule}{2mm}
\setlength{\fboxsep}{2mm}
\begin{document}\noindent{\color{red}%
\fbox{%
\begin{minipage}[t]{0.5\textwidth-2\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}\hspace{-\fboxrule}%
\fbox{%
\begin{minipage}[t]{0.5\textwidth-\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}}
\end{document}

a tabular will do the same ...

Answer 2

This is the final solution based on Herbert's answer with a bit adjustment.

\documentclass{article}
\usepackage[a4paper,margin=10mm,showframe]{geometry}
\usepackage{lipsum,calc,xcolor}
\setlength{\fboxrule}{2mm}
\setlength{\fboxsep}{2mm}
\begin{document}\noindent{\color{red}%
\fbox{%
\begin{minipage}[t]{0.5\textwidth-1.5\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}\hspace{-\fboxrule}%
\fbox{%
\begin{minipage}[t]{0.5\textwidth-1.5\fboxrule-2\fboxsep}
\color{blue}\lipsum[1]
\end{minipage}}}
\end{document}

This is the final solution based on @Herbert's solution. I made a small correction in his calculation.