So we only have 5 spots, but 15 bands to fill those spots.
For the first spot, we can choose from any of the 15 bands, so we have 15 choices.
For the second spot, we can choose from the 14 remaining bands (because we already chose one for the first spot), so we have 14 choices.
For the third spot, by similar reasoning as above, we have 13 choices; for the fourth spot, 12 choices; and for the last spot, we have 11 choices.
We realize that for each of the 15 possible bands in the first spot, we still have 14 possible bands for the second spot, and so on. Thus, we know to multiply instead of add.
Our answer is: 15 * 14 * 13 * 12 * 11 = 360,360