Explanation

(d)
Since, $\alpha$ and $\beta$ are the roots of equation $(x - a)(x - b) = 5$
Or $x^{2} - (a + b)x + ab - 5 = 0$
Then, $\alpha + \beta = (a + b)$ and $\alpha\beta = ab - 5$
$\therefore\ \ \ (x - \alpha)(x - \beta) + 5 = 0$ (given)
$\Rightarrow \ \ x^{2} - (\alpha + \beta)x + \alpha\beta + 5 = 0$
$\Rightarrow \ \ x^{2} - (a + b)x + ab - 5 + 5 = 0$
$\Rightarrow (x - a)(x - b) = 0$
Hence, $a$ and $b$ are the roots of equation
$(x - \alpha)(x - \beta) + 5 = 0$