To find the distance between the two 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, \((x_1, y_1) = (3, -5)\) and \((x_2, y_2) = (-2, -7)\).
First, we calculate the differences in the coordinates:
\[ x_2 - x_1 = -2 - 3 = -5 \]
\[ y_2 - y_1 = -7 - (-5) = -7 + 5 = -2 \]
Now we can plug these values into the distance formula:
\[ d = \sqrt{(-5)^2 + (-2)^2} \]
Calculating the squares:
\[ d = \sqrt{25 + 4} = \sqrt{29} \]
Now we need to calculate \(\sqrt{29}\).
Using a calculator, we find:
\[ \sqrt{29} \approx 5.385 \]
Rounding \(5.385\) to the nearest tenth gives:
\[ 5.4 \]
Thus, the distance between the points \((3, -5)\) and \((-2, -7)\) rounded up to the nearest tenth of a unit is approximately:
\[ \boxed{5.4} \text{ units} \]