5. Option 1.

Petya is the oldest child in the family. He has two sisters, Anya and Katya, and a brother Vasya. Petya calculated that Anya and Katya together are 19 years old, and Anya and Vasya together are 14 years old. Determine how old Katya is, if it is known that the two youngest children together are 7 years old.
Solution. Pete cannot be among the two younger children, and among the remaining children, the unconsidered pair is Katya and Vasya, so together they are 7 years old. If you add Katya's age to Anya's age, it will be 5 years more than if you add Vasya's age to Anya's age, so Anya is 5 years older than Vasya. But together, Katya and Vasya are 7 years old. Therefore, Katya is 6 years old, and Vasya is 1 year old.