Explanation

(b)
Let $f(x) = x^{2} - 2kx + k^{2} + k - 5$
Since, both roots are less than 5
Then, $D \geq 0,\ - \frac{b}{2a} < 5$ and $f(5) > 0$
Now, $D = 4k^{2} - 4\left( k^{2} + k - 5 \right) = - 4k + 20 \geq 0$
$\Rightarrow \ \ \ \ k \leq 5$ ...(i)
$- \frac{b}{2a} < 5\ \ \Rightarrow \ \ k < 5$ ...(ii)
And $f(5) > 0$
$\Rightarrow \ \ 25 - 10k + k^{2} + k - 5 > 0$
$\Rightarrow \ \ (k - 5)(k - 4) > 0$
$\Rightarrow \ \ k > 4$ and $k > 5$ ...(iii)
From Eqs. (i), (ii) and (iii), we get
$k < 4$