This question is actually based on a modified version of this answer. The original solution works perfectly well.
However, I wanted to add the word Case before the number and a comma after the number. While the word before the number works, a comma after the number throws an error which I have failed to solve.
Here is the modified source:
\documentclass{scrbook}
\usepackage{enumitem}
\newcounter{descriptcount}
\newlist{enumdescript}{description}{1}
\setlist[enumdescript,1]{%
before={\setcounter{descriptcount}{0}%
\renewcommand*\thedescriptcount{\arabic{descriptcount}}},
font=\bfseries\stepcounter{descriptcount}Case \thedescriptcount,~
}
\begin{document}
\begin{enumdescript}
\item item one
\item item two
\item[Some Text] item three
\item item four
\item item five
\end{enumdescript}
\end{document}
This generates an error,
! Missing \endcsname inserted. <to be read again> \protect l.15 \item item one ?
If the comma after \thedescriptcount is removed, it will work perfectly.

font={....,~}– Feb 04 '17 at 13:35