1. The problem asks to write an absolute value equation with the vertex at $(-5,-7)$. 2. The general form of an absolute value function with vertex $(h,k)$ is $$y = a|x - h| + k$$ where $a$ controls the slope of the arms and $h,k$ is the vertex. 3. Here, the vertex is $(-5,-7)$, so $h = -5$ and $k = -7$. Substitute these values: $$y = a|x - (-5)| - 7 = a|x + 5| - 7$$ 4. Without additional information about the slope, the simplest form assumes $a=1$: $$y = |x + 5| - 7$$ 5. This equation has a vertex at $(-5,-7)$ and opens upwards with slope 1 on both sides. Final answer: $$y = |x + 5| - 7$$