$x^2 - (5-k) x + (k+2) = 0 $ has two distinct real roots.

So, in the markscheme of this question, they take the discriminant ($-b^2 + 4ac$) and say it is greater than 0. That is, $( (-(5-k)^2 - 4(1)(k+2) > 0)$. 

Then, they take its discriminant and say it is less than 0.

$36 - (4 \* 32) < 0 $

And ,then they say it is true. I didn't understand how taking the discriminant of the discriminant helped prove.