5. At $17-00$ the speed of the racing car was 30 km/h. Every 5 minutes thereafter, the speed increased by 6 km/h. Determine the distance traveled by the car from $17-00$ to $20-00$ of the same day.
5. Let's write down the sequence of numbers expressing the speed at which the car was traveling on the highway: $30,36,42,48,54 \ldots 240$. To determine the distance, we need to calculate the sum:

$$
\begin{aligned}
30: 12 & +36: 12+42: 12+\ldots .+234: 12+240: 12= \\
& =(30+36+42+. .+234+240): 12
\end{aligned}
$$

If we add the first and last terms, the second and second-to-last terms, and other similar pairs of numbers, we will always get $270(30+240=36+234=42+228$ and so on). Let's determine how many such pairs there are. The speed increased 12 times every hour ( $60: 5=12$ ). Over three hours, it increased 36 times. Therefore, there are 18 such pairs. To determine the distance, we multiply 270 by 18 and divide by 12. We get 405 km $(270 \times 18: 12=4860: 12=405)$.

Answer: 405 km.