set hanging indent for more than one paragraph at a time

This is a simple solution to your problem, when the paragraphs contain only text.

\documentclass{article}
\usepackage[numbers]{kantlipsum}
\begin{document}

\parindent=0pt
\newcounter{paras}
\everypar{%
  \stepcounter{paras}%
  \ifnum\value{paras}>10 
    \everypar{}
  \else
    \hangindent=5em \hangafter=1
  \fi}

\kant[1-100]

\end{document}

The mysterious \everypar is a container of tokens that are inserted whenever a paragraph is started. In this case we say to step the counter and look at its value: at the moment its value is greater than 10, we are at the 11th paragraph, so we remove everything from \everypar, otherwise we set the hanging indentation.

I am sure it is possible by some TeX programming. On the other hand, the hanging package already does most of what you are asking for. Just put all body text, or any number of paragraphs to be hung, inside a \hangparas environment.