To horizontally shift the function $g(x) = -2x^2 + 6x - 8$ to the left by 5 units, you replace $x$ with $x + 5$ in the function.

The new function after the horizontal shift is:

$g(x) = -2(x + 5)^2 + 6(x + 5) - 8$

Now, let's expand and simplify the expression:

1. Expand $(x + 5)^2$: $(x + 5)^2 = x^2 + 10x + 25$

2. Substitute back into the function: $g(x) = -2(x^2 + 10x + 25) + 6(x + 5) - 8$

3. Distribute the