How to Mark Right Angle in Tikz

You can use also tkz-euclide:

\documentclass[11pt]{exam} 
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document} 
    \begin{tikzpicture} 
        \coordinate (A) at (-5, 0) {};
        \coordinate (B) at (5, 0) {};
        \coordinate (C) at (0, 5) {};
        \coordinate (0) at (0, 0) {};

        % left angle
        \tkzMarkRightAngle[draw=blue,size=.7](A,0,C);
        \tkzLabelAngle[dist=.5](A,0,C){$\alpha$};

        % right angle
        \tkzMarkRightAngle[draw=red,size=.7](B,0,C);
        \tkzLabelAngle[dist=.5](B,0,C){$\beta$};

        % axis lines
        \tkzDrawLines[add=0 and 0, arrows=->](A,B 0,C)

    \end{tikzpicture}
\end{document}

You can use perpendicular syntax. It saves typing the coordinate at corner.

\documentclass[tikz,border=2mm]{standalone} 
\usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture}
\draw (-5,0) -- (5,0);
\draw (0,0) -- (0,5);

\draw (-.3,0)|-(0,.3) (0,.5)-|(.5,0);
\end{tikzpicture}
\end{document}