Four buddies bought a ball. First one paid half of the ball price. Second one gave one third of money that other three gave. Third one paid a quarter of sum paid by other three. Fourth paid $5\$$. How much did the ball cost?
1. Let the total cost of the ball be \( C \).

2. The first person paid half of the ball price:
   \[
   \text{First person's payment} = \frac{C}{2}
   \]

3. The second person gave one third of the money that the other three gave. Let \( x \) be the amount the second person paid. Then:
   \[
   x = \frac{1}{3} \left( \frac{C}{2} + y + 5 \right)
   \]
   where \( y \) is the amount the third person paid.

4. The third person paid a quarter of the sum paid by the other three. Let \( y \) be the amount the third person paid. Then:
   \[
   y = \frac{1}{4} \left( \frac{C}{2} + x + 5 \right)
   \]

5. The fourth person paid $5:
   \[
   \text{Fourth person's payment} = 5
   \]

6. Summing up all the payments, we have:
   \[
   \frac{C}{2} + x + y + 5 = C
   \]

7. Substitute \( x \) and \( y \) from steps 3 and 4 into the equation in step 6:
   \[
   \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + y + 5 \right) + \frac{1}{4} \left( \frac{C}{2} + x + 5 \right) + 5 = C
   \]

8. Simplify the equation:
   \[
   \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + \frac{1}{4} \left( \frac{C}{2} + x + 5 \right) + 5 \right) + \frac{1}{4} \left( \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + y + 5 \right) + 5 \right) + 5 = C
   \]

9. Solving the above equation step-by-step, we find:
   \[
   \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + \frac{1}{4} \left( \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + y + 5 \right) + 5 \right) + 5 \right) + \frac{1}{4} \left( \frac{C}{2} + \frac{1}{3} \left( \frac{C}{2} + \frac{1}{4} \left( \frac{C}{2} + x + 5 \right) + 5 \right) + 5 \right) + 5 = C
   \]

10. After simplifying, we find:
    \[
    \frac{C}{2} + \frac{C}{6} + \frac{C}{12} + 5 = C
    \]

11. Combine the terms:
    \[
    \frac{6C + 2C + C}{12} + 5 = C
    \]
    \[
    \frac{9C}{12} + 5 = C
    \]
    \[
    \frac{3C}{4} + 5 = C
    \]

12. Solving for \( C \):
    \[
    5 = C - \frac{3C}{4}
    \]
    \[
    5 = \frac{C}{4}
    \]
    \[
    C = 20
    \]

13. The ball cost is:
    \[
    \boxed{20}
    \]