To find the distance between the points \((-5, 5)\) and \( (4, -7)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-5, 5)\) and \((x_2, y_2) = (4, -7)\).
Now, substitute the coordinates into the formula:
\[ d = \sqrt{(4 - (-5))^2 + (-7 - 5)^2} \]
Calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\[ x_2 - x_1 = 4 + 5 = 9 \] \[ y_2 - y_1 = -7 - 5 = -12 \]
Now substitute these values back into the formula:
\[ d = \sqrt{(9)^2 + (-12)^2} \] \[ d = \sqrt{81 + 144} \] \[ d = \sqrt{225} \] \[ d = 15 \]
Thus, the distance between the two points is \(15\). Since \(15\) rounded to the nearest tenth is still \(15.0\), we can present the final answer as:
\[ \boxed{15.0} \]