5.1. (14 points) The old man was pulling the turnip, and one by one, the old woman, the granddaughter, the dog, and the cat joined him. They pulled and pulled, but couldn't pull out the turnip! The cat called the mouse. They pulled and pulled, and finally pulled out the turnip! It is known that each subsequent participant pulls with a quarter of the strength of the previous one. How many men from the village, pulling with the same strength as the old man, should have been called to help the old man and the cat pull out the turnip?
Answer: 2.

Solution. The old woman, the granddaughter, Zhuchka, and the mouse pull with a combined force of

$$
\frac{3}{4}+\left(\frac{3}{4}\right)^{2}+\left(\frac{3}{4}\right)^{3}+\left(\frac{3}{4}\right)^{5}=\frac{2019}{1024}=1 \frac{995}{1024}
$$

of the force of the old man. Therefore, two men need to be called.