Answer
12.3 years.
Work Step by Step
If original activity $N_{0}=100$
Then, present activity $N=100-5.5=94.5$
Time $t=1\,year$
$\ln(\frac{N_{0}}{N})=kt$ where $k$ is the rate constant.
$\implies \ln(\frac{100}{94.5})=0.05657=k\times1\,y$
Or $k= \frac{0.05657}{1\,y}=0.05657\,y^{-1}$
$t_{1/2}=\frac{0.693}{0.05657\,y^{-1}}=12.3\,y$