4. Road problem. Can 13 cities be connected by roads so that exactly 5 roads lead out of each city?
4. Since 5 roads lead out of each city, the total number of roads is 65. Note that in this case, each road $AB$ is counted twice, as leading out of cities $A$ and $B$. Thus, the total number of roads should be even. This leads to a contradiction. Answer: it is impossible.