The problem asks us to evaluate the expression $(5 + \sqrt{-1})(2 - \sqrt{-36})$.

1. Problem Description

The problem asks us to evaluate the expression $(5 + \sqrt{-1})(2 - \sqrt{-36})$.

2. Solution Steps

First, we simplify the square roots of negative numbers using the definition of the imaginary unit $i = \sqrt{-1}$.

$\sqrt{-1} = i$

$\sqrt{-36} = \sqrt{36 \cdot -1} = \sqrt{36} \cdot \sqrt{-1} = 6i$

Now substitute these values into the expression:

$(5 + i)(2 - 6i)$

Next, we expand the product using the distributive property (FOIL method):

$(5 + i)(2 - 6i) = 5(2) + 5(-6i) + i(2) + i(-6i)$

$= 10 - 30i + 2i - 6i^2$

Since $i^2 = -1$, we have:

$10 - 30i + 2i - 6(-1) = 10 - 30i + 2i + 6$

Combine the real and imaginary parts:

$(10 + 6) + (-30i + 2i) = 16 - 28i$

3. Final Answer

$16 - 28i$