To find the distance between the points \((3, -5)\) and \((-2, -7)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, let \((x_1, y_1) = (3, -5)\) and \((x_2, y_2) = (-2, -7)\).
First, we calculate the differences in the x-coordinates and y-coordinates:
\[ x_2 - x_1 = -2 - 3 = -5 \] \[ y_2 - y_1 = -7 - (-5) = -7 + 5 = -2 \]
Now we can substitute these values into the distance formula:
\[ d = \sqrt{(-5)^2 + (-2)^2} \]
Calculating the squares:
\[ (-5)^2 = 25 \] \[ (-2)^2 = 4 \]
Adding these together gives:
\[ d = \sqrt{25 + 4} = \sqrt{29} \]
Next, we calculate \(\sqrt{29}\). The approximate value of \(\sqrt{29}\) is about \(5.385\).
Finally, rounding \(5.385\) to the nearest tenth, we get:
\[ 5.4 \]
Thus, the distance between the points \((3, -5)\) and \((-2, -7)\), rounded to the nearest tenth, is:
\[ \boxed{5.4} \]