5. On the website of the football club "Rostov," a poll is being conducted to determine which of the $m$ football players the website visitors consider the best at the end of the season. Each visitor votes once for one player. The website displays the rating of each player, which is the percentage of votes cast for them, rounded to the nearest whole number. After several visitors have voted, the total rating of the nominees was $95 \%$. What is the smallest $m$ for which this is possible?
Solution. Let $a$ be the greatest loss of a percentage point due to rounding when determining a footballer's rating. Then, according to rounding rules, $aa m \geqslant 5$, which means $0.5 m>5$ or $m>10$.

We will show that a solution exists when $m=11$. For example, let $m=11$ and 73 visitors voted, with 33 of them voting for one footballer, while the remaining 40 visitors evenly distributed their votes among 10 footballers, giving each 4 votes. In this case, the total rating is

$\frac{33}{73} \cdot 100 \%+10 \cdot \frac{4}{73} \cdot 100 \approx 45 \%+10 \cdot 5 \%=95 \%$.

Thus, the minimum $m=11$. Answer: 11.