The problem asks to evaluate the expression $(-5 + \sqrt{-4}) + (3 - \sqrt{-16})$.

1. Problem Description

The problem asks to evaluate the expression $(-5 + \sqrt{-4}) + (3 - \sqrt{-16})$.

2. Solution Steps

First, we simplify the square roots of negative numbers.

$\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i$

$\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i$

Now, substitute these values back into the original expression:

$(-5 + 2i) + (3 - 4i)$

Next, we combine the real and imaginary parts separately:

$(-5 + 3) + (2i - 4i)$

$-2 - 2i$

3. Final Answer

$-2 - 2i$