Answer
34.8 days
Work Step by Step
If Original activity $N_{0}=100$, then present activity $N=5.0$.
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{8.04\,day}=0.086194/day$
$\ln(\frac{N_{0}}{N})=kt$ where $t$ is the time required.
$\implies \ln(\frac{100}{5.0})=2.9957=(0.086194/day)\times t$
Or $t= \frac{2.9957}{0.086194/day}= 34.8\,days$
