To find the center of the original circle given the equation \( 16 - (x + 2)^2 - (y - 5)^2 = 0 \), we can rewrite it in standard form.
Starting from the equation:
\[ 16 - (x + 2)^2 - (y - 5)^2 = 0 \]
We can rearrange it to the standard form of a circle:
\[ (x + 2)^2 + (y - 5)^2 = 16 \]
Here, we see that the center of the circle is at:
\[ (-2, 5) \]
Now, the circle is translated 3 units to the right and 3 units up.
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Translating 3 units to the right means adding 3 to the x-coordinate: \(-2 + 3 = 1\)
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Translating 3 units up means adding 3 to the y-coordinate: \(5 + 3 = 8\)
Thus, the new center of the translated circle is at:
\[ (1, 8) \]
Therefore, the center of the translated circle is \(\boxed{(1, 8)}\).