The problem asks for the equation of a line parallel to $y = -x + 5$ that passes through the point $(8, -6)$.

Since parallel lines have the same slope, the slope of the new line will also be $-1$ (since the slope of $y = -x + 5$ is $-1$).

Using the point-slope form equation $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is the given point:

$y - (-6) = -1(x - 8)$

Simplifying:

$y + 6 = -1(x - 8)$

The correct equation is $y + 6 = -(x - 8)$, which matches the last option.

So, the answer is: $y + 6 = -(x - 8)$.