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To find the resulting coordinates after applying the translation vector, you need to add the components of the translation vector to the original coordinates.
The original coordinates are \((-2, -5)\) and the translation vector is \(\langle 2, -3 \rangle\).
You can calculate the new coordinates as follows:
\[
x' = x + \text{translation}_x = -2 + 2 = 0
\]
\[
y' = y + \text{translation}_y = -5 - 3 = -8
\]
Thus, the resulting coordinates after the translation are \((0, -8)\).