Let initial number of Nuclei is $N_0$

after t = 15 minutes amount of nuclei remaining is $\frac{N_0}{8}$

$ N = \frac{N_0}{2^n} = \frac{N_0}{8} = \frac{N_0}{2^3}$

$\Rightarrow n = \frac{t}{t_{\frac{1}{2}}} = 3$

$\Rightarrow t_\frac{1}{2} = \frac{t}{3} = 5 min$