Let's solve the problem step by step to find the speeds of the two trains.

1. Determine the relative speed:
When the trains are moving in the same direction, the relative speed is the difference in their speeds. When they are moving in opposite directions, the relative speed is the sum of their speeds.

Let's assume the speed of one train is 'x' m/s and the speed of the other train is 'y' m/s.

- When the trains are moving in the same direction, the relative speed is (x - y) m/s.
- When the trains are moving in opposite directions, the relative speed is (x + y) m/s.

2. Calculate the time taken to cross each other:
When the trains are moving in the same direction, the time taken to cross each other is given by the formula:
Time = Length of first train + Length of second train / Relative speed

Given that the length of the first train is 150 m and the length of the second train is 250 m, and the time taken is 20 seconds, we can write the equation as:
20 = (150 + 250) / (x - y)

Similarly, when the trains are moving in opposite directions, the time taken to cross each other is given by the formula:
Time = Length of first train + Length of second train / Relative speed

Given that the time taken is 5 seconds, we can write the equation as:
5 = (150 + 250) / (x + y)

3. Solve the equations:
We now have two equations:
20 = 400 / (x - y)
5 = 400 / (x + y)

Let's solve these equations simultaneously to find the values of 'x' and 'y'.

Multiplying the first equation by 4, we get:
80 = 1600 / (x - y)

Now, we can equate the right-hand sides of the two equations:
1600 / (x - y) = 400 / (x + y)

Cross-multiplying, we get:
1600(x + y) = 400(x - y)

Simplifying further, we have:
4(x + y) = x - y

Expanding and rearranging the equation, we get:
3x - 3y = 0

Dividing both sides by 3, we have:
x - y = 0

So, x = y

4. Substitute the value of 'x' in either of the equations:
Let's substitute x = y in the equation 5 = 400 / (x + y):

5 = 400 / (2x)

Multiplying both sides by 2x, we get:
10x = 400

Dividing both sides by 10, we have:
x = 40

Therefore, the speed of one train is 40 m/s.

Since x = y, the speed of the other train is also 40 m/s.

Thus, the correct answer is '40' for both train speeds. The given answer '272 and 211' does not seem correct based on the information provided in the question.