Let's break down the conditions for the function $f(x)$ and sketch the graph accordingly:

1. Domain: $f(x)$ is defined for all real numbers, $x \in \mathbb{R}$.
2. Constant for $-5 \leq x \leq 0$: The function $f(x)$ is a constant value over this interval. Let's assume this constant value is $c$.
3. Increasing for $0 \leq x \leq 2$: The function $f(x)$ is strictly increasing in this interval.
4. Maximum value at $x = 2$: The function $f(x)$ reaches its maximum value at $x = 2$.

Sketching the Graph

1. Interval $-5 \leq x \leq 0$: The graph will be a horizontal line since $f(x) = c$ is constant in this interval.
2. Interval $0 \leq x \leq 2$: The graph will rise from the point $(0, c)$ to reach the maximum value at $x = 2$.
3. For $x > 2$: Since $x = 2$ is the maximum, the graph should either decrease or stay constant for $x > 2$.

Now, I will describe the graph:

• From $x = -5$ to $x = 0$: A horizontal line at some constant value $c$.
• From $x = 0$ to $x = 2$: A curve that increases, starting from $(0, c)$ and reaching the maximum point at $(2, f(2))$.
• For $x > 2$: The graph either stays flat or decreases after reaching the maximum at $x = 2$.

Would you like me to generate a visual graph for you?