(Note: I agree that the writeups that follow mine prove me wrong. For the sake of the references made in other writeups, I am keeping this as is)

I am sorry to say, but this is an incorrect solution. The organization of the previous test tubes is as follows:

1
2 **12**
**3** 11
**4** 10
5 **9**
6 **8**
7

This leaves the 12 side weighing less than the 3/4 or 8/9 sides. Therefore, the centerfuge will rock out of orbit due to the force of the two heavier sides. As a result, it will vibrate its way across the labtable onto the floor. The only way to make 5 tubes fit is to put 4 in equally (3,6,9,12) and place the 5th one in the center, if the centerfuge can hold it.