5) Until 2013, in the penal colony of Zoranel, the population was $60 \%$ androids, of which $5 \%$ were assigned to surveillance; let's say $q$ is the percentage of surveillance androids out of the total population in that year. In 2014, the population increased by $10 \%$ due to the arrival of $N$ exiled humans. By how much did the percentage of surveillance androids on the total population decrease? $\begin{array}{lll}\text { (A) did not change } & \text { (B) by less than a tenth of } q & \text { (C) by more than a tenth of } q\end{array}$ (D) depends on $N \quad$ (E) depends on how large the initial population was.
5. The answer is $\mathbf{( B )}$.

Let $P$ be the population of Zoranel up to 2013. The percentage of surveillance androids in the total population in that year was $q=\frac{5}{100} \frac{60}{100}=\frac{3}{100}$, and the number of such surveillance androids was $q P$. After the arrival of the exiles, the population rose to $P^{\prime}=P+\frac{10}{100} P=\frac{11}{10} P$, while the percentage of surveillance androids in the total population dropped to $q^{\prime}=\frac{q P}{P^{\prime}}=q \frac{10}{11}$. Therefore, the percentage decreased by $q-q^{\prime}=\frac{1}{11} q$, which is less than $\frac{1}{10} q$.

[Problem proposed by A. Sambusetti]