**Solution:**

Let's assume the length of the train as 'L' meters.

When the train passes a person walking in the opposite direction at a speed of 5 m/s, it covers a distance equal to the sum of the lengths of the train and the distance covered by the person, which is equal to (L + 5) meters.

Similarly, when the train passes another person walking in the opposite direction at a speed of 10 m/s, it covers a distance equal to the sum of the lengths of the train and the distance covered by the person, which is equal to (L + 10) meters.

Now, we are given that the time taken by the train to cover both the distances is 6 seconds and 5 seconds, respectively.

Using the equation: Speed = Distance/Time, we can write the following equations:

- For the first person: (L + 5)/6 = 5
- For the second person: (L + 10)/5 = 10

**Solving the equations:**

- (L + 5)/6 = 5
=> L + 5 = 5 * 6
=> L + 5 = 30
=> L = 30 - 5
=> L = 25 meters

- (L + 10)/5 = 10
=> L + 10 = 10 * 5
=> L + 10 = 50
=> L = 50 - 10
=> L = 40 meters

Therefore, the length of the train is 25 meters.

**Explanation:**

When the train passes a person walking in the opposite direction at a speed of 5 m/s, the relative speed between the train and the person is the sum of their individual speeds, which is (5 + 5) = 10 m/s. The train takes a time of 6 seconds to cover the distance equal to the sum of their lengths, which is (L + 5) meters. Therefore, we can write the equation as (L + 5)/6 = 10.

Similarly, when the train passes another person walking in the opposite direction at a speed of 10 m/s, the relative speed between the train and the person is the sum of their individual speeds, which is (10 + 10) = 20 m/s. The train takes a time of 5 seconds to cover the distance equal to the sum of their lengths, which is (L + 10) meters. Therefore, we can write the equation as (L + 10)/5 = 20.

Solving the equations, we find that the length of the train is 25 meters.