The remainder after dividing x4 + 3x3 - 8x2 + 5x - 9 by x + 5 is

(x^4+3x^3-8x^2+5x-9) / (x+5)

x^3 remainder - 2x^3-8x^2+5x-9

-2x^2 remainder 2x^2+5x-9

2x remainder - 5x-9

-5 remainder 16

(x+5) (x^3-2x^2+2x-5) + 16 / (x+5)

so the remainder after division is:

16 / (x+5)