The problem states that a system has energy levels E0, 2E0, 3E0, and so on, where the excited states are triply degenerate. This means that each energy level has three possible states associated with it. We are given that three non-interacting bosons are placed in the system, and the total energy of these bosons is 5E0. We need to determine the number of microstates for this system.

Understanding the Problem
To solve this problem, we need to consider the energy distribution among the three bosons. The bosons can occupy different energy levels, but since they are non-interacting, the order of their occupation does not matter. We can think of this as distributing the energy among the three bosons in different ways.

Calculating the Number of Microstates
To find the number of microstates, we need to count all possible ways of distributing the energy of 5E0 among the three bosons. Let's consider the different possibilities:

1. If all three bosons occupy the lowest energy level E0, there is only one microstate.
2. If two bosons occupy the lowest energy level E0 and one boson occupies the next energy level 2E0, there are three possible ways to choose which boson occupies the higher energy level. Within each choice, there are three possible microstates due to the degeneracy of the excited state. Therefore, there are a total of 3 * 3 = 9 microstates.
3. If one boson occupies the lowest energy level E0 and two bosons occupy the next energy level 2E0, there are three possible ways to choose which boson occupies the lower energy level. Within each choice, there are three possible microstates due to the degeneracy of the excited state. Therefore, there are a total of 3 * 3 = 9 microstates.
4. If all three bosons occupy the next energy level 2E0, there is only one microstate.

Adding up the number of microstates from each possibility, we have a total of 1 + 9 + 9 + 1 = 20 microstates.

Conclusion
The correct answer is 20 microstates.