Basta inserir o ponto (5,5) na hora de definir o \draw. Segue o código:
\begin{document}
\begin{center}
\begin{tikzpicture}[scale=1]
\draw[->, very thick] (-0.1,0) -- (8,0) node[right]{$x_1$};
\draw[->, very thick] (0,-0.1) -- (0,8) node[above]{$x_2$};
\draw (0,7.5) -- (5,5) -- (7.5,0)node[below]{$7,5$};
\node[left] at (0,7.5){$7,5$};
\draw[dashed] (5,5) -- (5,0);
\draw[dashed] (5,5) -- (0,5);
\node[below] at (3,0){$5$};
\node[left] at (0,4){$5$};
\end{tikzpicture}
\end{center}
\end{document}