\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{knots}
\begin{document}
\begin{tikzpicture}
\definecolor{blue1}{RGB}{0,129,188}
\definecolor{yellow1}{RGB}{252,177,49}
\definecolor{black1}{RGB}{35,34,35}
\definecolor{green1}{RGB}{0,157,87}
\definecolor{red1}{RGB}{238,50,78}
\begin{knot}[clip width=1.5pt]
    \strand[line width=0.25cm,red1] (3,0) circle(1.25cm);
    \strand[line width=0.25cm,green1] (1.5,-1.375) circle(1.25cm);
    \strand[line width=0.25cm,black1] (0,0) circle(1.25cm);
    \strand[line width=0.25cm,yellow1] (-1.5,-1.375) circle(1.25cm);
    \strand[line width=0.25cm,blue1] (-3,0) circle(1.25cm);
    \flipcrossings{2,4,6,8}
\end{knot}
\end{tikzpicture}
\end{document}

第二个方法,使用pstricks来进行绘制。 这里需要用到http://comedy.dante.de/~herbert/texnik/tex/generic/pstricks-add/pstricks-add.tex

\documentclass{article}
\usepackage{pstricks-add}
\pagestyle{empty}
\begin{document}

\begin{pspicture}(-4.5,-3)(4.5,1.5)
\psOlympicRings(0,0)
\psOlympicRings[psscale=0.2](1.5,-1.5)
\psOlympicRings[psscale=0.2](-1.5,-1.5)
\end{pspicture}

\end{document}

效果图:Olympic_Rings选自:https://tex.stackexchange.com/questions/323689/how-to-get-rid-of-the-almost-invisible-faint-lines-in-the-olympic-rings#comment790506_323693

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