First, we sample the $5$ types. That leaves space for $8$ more, which we can choose freely, with repetition. The dots-and-bars(stars and bars) formula tells us that there are
$$
\left(\begin{array}{c}
8+5-1 \\
5-1
\end{array}\right)=\left(\begin{array}{c}
12 \\
4
\end{array}\right)
$$
ways to do this.