since (x-5) is a factor of f(x)= kx^3 – 17x^2 - 4kx + 5 we can write

kx^3 – 17x^2 - 4kx + 5 = (x - 5) q(x), where q(x) is a polynomial of degree 2

if x = 5 the right side of the above equation is 0 so is the left that is x = 5 is a null of the function f(x)

f(5) = 0

k5^3 – 17*5^2 - 4k*5 + 5 = 0

125k - 425 - 20k + 5 = 0

105k - 420 = 0

k = 420/105

k = 4