Yes, that is correct.
Even though there are $5!=120$ ways of physically doing it, many of them are equivalent (and you rightly corrected this by dividing by $3!2!$).
Look at them to convince yourself. The 10 distinct ways are listed below.
\begin{gather*}{\color{orange}P}{\color{orange}P}{\color{orange}P}{\color{gray}N}{\color{gray}N}\\
{\color{orange}P}{\color{orange}P}{\color{gray}N}{\color{orange}P}{\color{gray}N}\\
{\color{orange}P}{\color{orange}P}{\color{gray}N}{\color{gray}N}{\color{orange}P}\\
{\color{orange}P}{\color{gray}N}{\color{orange}P}{\color{orange}P}{\color{gray}N}\\
{\color{orange}P}{\color{gray}N}{\color{orange}P}{\color{gray}N}{\color{orange}P}\\
{\color{orange}P}{\color{gray}N}{\color{gray}N}{\color{orange}P}{\color{orange}P}\\
{\color{gray}N}{\color{orange}P}{\color{orange}P}{\color{orange}P}{\color{gray}N}\\
{\color{gray}N}{\color{orange}P}{\color{orange}P}{\color{gray}N}{\color{orange}P}\\
{\color{gray}N}{\color{orange}P}{\color{gray}N}{\color{orange}P}{\color{orange}P}\\
{\color{gray}N}{\color{gray}N}{\color{orange}P}{\color{orange}P}{\color{orange}P}
\end{gather*}