We have,

p (x) = x³ – 20x + 5k

It is given in the question that, (x + 5) is a factor of p (x) so:

p (- 5) = 0

(- 5)³ – 20 (- 5) + 5 k = 0

- 125 + 100 + 5k = 0

- 25 + 5k = 0

5k = 25

k =

k = 5

Hence, option B is correct