To find the slope of the line represented by the equation \( y + 2.5 = -3(x - 5) \), we can first rewrite it in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope.
Starting with the given equation:
\[ y + 2.5 = -3(x - 5) \]
Distributing the \(-3\) on the right side:
\[ y + 2.5 = -3x + 15 \]
Next, we isolate \( y \) by subtracting \( 2.5 \) from both sides:
\[ y = -3x + 15 - 2.5 \]
Simplifying the right side:
\[ y = -3x + 12.5 \]
Now, in the form \( y = mx + b \), the slope \( m \) is \(-3\).
Therefore, the slope of the line is:
\[ \boxed{-3} \]