To divide two complex numbers, we first need to multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of -1+4i is -1-4i.

So, let's multiply the numerator and denominator by the conjugate:

((-9 + 8i + 5 - 8i) (-1 - 4i)) / ((-1 - 4i) (-1 + 4i))

Simplify the numerator:

((-4) (-1) + (8i) (-1) + (5) (-1) + (8i) (-4i))

Multiplying:

(4 - 8i - 5 - 32i^2)

Since i^2 = -1,

(4 - 8i - 5 + 32)

(-1 + 24 - 8i)

(23 - 8i)

The denominator simplifies to:

((-1) (-1) - (4i) (4i))

(1 + 16)

(17)

Therefore, the division simplifies to:

(23 - 8i) / 17