1. The problem asks for the value of the Dirichlet function at $x = -5$. 2. The Dirichlet function $D(x)$ is defined as: $$ D(x) = \begin{cases} 1 & \text{if } x \in \mathbb{Q} \\ 0 & \text{if } x \in \mathbb{R} \setminus \mathbb{Q} \end{cases} $$ This means the function equals 1 if $x$ is rational and 0 if $x$ is irrational. 3. To find $D(-5)$, we check if $-5$ is rational. 4. Since $-5$ is an integer, and all integers are rational numbers, $-5 \in \mathbb{Q}$. 5. Therefore, by the definition of the Dirichlet function, $D(-5) = 1$. Final answer: $D(-5) = 1$.