There are five people, and the age differences (absolute value) for each twosome are all different. Find the smallest possible difference in age between the oldest and the youngest.
1. **Define the variables and constraints:**
   Let the ages of the five people be \(a, b, c, d, e\) such that \(a > b > c > d > e\). We need to ensure that the absolute differences between each pair are all distinct.

2. **Calculate the number of differences:**
   There are \(\binom{5}{2} = 10\) pairs, so we need 10 distinct differences.

3. **Determine the minimum possible difference \(a - e\):**
   Since there are 10 distinct differences, the smallest possible set of differences is \(\{1, 2, 3, \ldots, 10\}\). The sum of these differences is:
   \[
   S = 1 + 2 + 3 + \cdots + 10 = \frac{10 \cdot 11}{2} = 55
   \]

4. **Express the sum of differences in terms of \(a, b, c, d, e\):**
   The sum of the differences can be written as:
   \[
   S = (a - b) + (a - c) + (a - d) + (a - e) + (b - c) + (b - d) + (b - e) + (c - d) + (c - e) + (d - e)
   \]

5. **Simplify the expression:**
   Grouping the terms, we get:
   \[
   S = 4a + 3b + 2c + d - (4e + 3d + 2c + b) = 4(a - e) + 2(b - d) + (b - d)
   \]
   This simplifies to:
   \[
   S = 4(a - e) + 3(b - d)
   \]

6. **Check if \(a - e = 10\) is possible:**
   If \(a - e = 10\), then:
   \[
   S = 4 \cdot 10 + 3(b - d) = 40 + 3(b - d)
   \]
   For \(S\) to be 55, we need:
   \[
   40 + 3(b - d) = 55 \implies 3(b - d) = 15 \implies b - d = 5
   \]
   However, this does not ensure all differences are distinct, and it is not possible to have all 10 distinct differences.

7. **Check if \(a - e = 11\) is possible:**
   If \(a - e = 11\), we can try specific values:
   \[
   (a, b, c, d, e) = (x + 11, x + 9, x + 4, x + 1, x)
   \]
   The differences are:
   \[
   \begin{aligned}
   &a - b = 2, \\
   &a - c = 7, \\
   &a - d = 10, \\
   &a - e = 11, \\
   &b - c = 5, \\
   &b - d = 8, \\
   &b - e = 9, \\
   &c - d = 3, \\
   &c - e = 4, \\
   &d - e = 1
   \end{aligned}
   \]
   These differences are all distinct and sum to 55.

Conclusion:
The smallest possible difference in age between the oldest and the youngest is 11.

The final answer is \(\boxed{11}\)