The half life of a radioactive substance is 5 years. After x years...

6 . 25 %$of the initial value means, final number of nuclei should be, \left(\dfrac{{N}_{0}}{16}\right)$.

Number of nuclei remaining after $n$ half lives is $N = \dfrac{{N}_{0}}{{2}^{n}}$
$6 . 25$
$\dfrac{6 . 25}{100}{N}_{0} = \dfrac{{N}_{0}}{{2}^{n}} ⇒ \dfrac{625}{{10}^{4}} = \dfrac{1}{{2}^{n}}$
$⇒ {2}^{n} = \dfrac{{10}^{4}}{{5}^{4}} ⇒ {2}^{n} = {2}^{4}$
$⇒ n = 4$

Therefore, time taken will be, $n \times t\dfrac{1}{2} = 4 \times 5 = 20years$