Let the two positive numbers be $x$ and $y.$
According to the question, $x + y = 100 \quad \rightarrow (1)$
And, $(x-5) \cdot (y – 5) = 0$
$\implies xy -5x – 5y + 25 = 0$
$\implies x(100 – x) – 5(100) + 25 = 0 \quad [\because \text{From equation (1)}]$
$\implies 100x – x^{2} – 500 + 25 = 0$
$\implies -x^{2} + 100x – 475 = 0$
$\implies x^{2} - 100x + 475 = 0$
$\implies x^{2} – 95x – 5x + 475 = 0$
$\implies x(x-95)-5(x-95) = 0$
$\implies (x-95)(x-5) = 0$
$\implies (x-95) = 0 \; \& \;(x-5) = 0$
Now, if $x = 95 \implies y = 5,$ and if $x = 5 \implies y = 95.$
$\therefore$ One of the original number is $95.$
$\textbf{PS:}$ If one number is non-zero, then another number is $5,$ so that when we subtract $5$ from each the product will be $0.$
So, the correct answer is $(D).$