Point D (–5, –5) and point E (3, 5) are located on a coordinate grid.

To calculate the distance between points D (-5, -5) and E (3, 5), we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1)\) are the coordinates of point D and \((x_2, y_2)\) are the coordinates of point E.

Substituting the values, we have:

\[
x_1 = -5, \quad y_1 = -5, \quad x_2 = 3, \quad y_2 = 5
\]

Now, calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[
x_2 - x_1 = 3 - (-5) = 3 + 5 = 8
\]
\[
y_2 - y_1 = 5 - (-5) = 5 + 5 = 10
\]

Now plug these into the distance formula:

\[
d = \sqrt{(8)^2 + (10)^2}
\]
\[
d = \sqrt{64 + 100}
\]
\[
d = \sqrt{164}
\]

Now, we can simplify \(\sqrt{164}\):

\[
\sqrt{164} \approx 12.81 \text{ (when calculated)}
\]

To find an approximate numerical value, we can round this:

Thus, the distance between points D and E is approximately **12.81 units**.