Step 1 :Given the five-number summary table for the number of years of experience for each teacher at Carlson High School: \begin{tabular}{ccccc} $\operatorname{Min}$ & $Q_{1}$ & Median & $Q_{3}$ & $\operatorname{Max}$ \\ \hline 2 & 5 & 8 & 11 & 16 \end{tabular}
Step 2 :We are asked to find the number of years of experience that about 25% of Carlson High School teachers have fewer than, which corresponds to the first quartile, $Q_1$. From the table, we can see that $Q_1 = 5$ years.
Step 3 :\boxed{5}