How to make \parshape work inside a tikz node?

Put the text in a \parbox:

Also it appears that you can use the font= to set the \parshape and then it just works (although I am not sure that this is a good idea).

Code:

\documentclass{article}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}
    \path node[draw,text width=50mm]
          {\parbox{\linewidth}{%
              \setlength{\parindent}{0pt}
                \parshape=3 5mm 40mm 10mm 35mm 15mm 30mm
                This is sentence 1. 
                This is sentence 2. 
                This is sentence 3. 
                This is sentence 4. 
                This is sentence 5.%
          }%
      };
  \end{tikzpicture}
\end{document}

Code:

\begin{document}
  \begin{tikzpicture}
    \path node[draw,text width=50mm, font={\parshape=3 5mm 40mm 10mm 35mm 15mm 30mm}]
       {%
            This is sentence 1. 
            This is sentence 2. 
            This is sentence 3. 
            This is sentence 4. 
            This is sentence 5.%
      };
  \end{tikzpicture}
\end{document}

Just introduce \par command will solve the issue:

\documentclass{article}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}
    \path node[draw,text width=50mm]
      { \setlength{\parindent}{0pt}
        \parshape=3 5mm 40mm 10mm 35mm 15mm 30mm
        This is sentence 1. This is sentence 2. This is sentence 3.
        This is sentence 4. This is sentence 5.\par
      };
  \end{tikzpicture}
\end{document}