You can assign the label "A" to any of the 5 members so you can do that in 5 ways. Once that has been done, there are 4 members not yet assigned so you can assign the label "G" in 4 ways, then assign the label "M" in 3 ways, then assign the label "S" in 2 ways: 5(4)(3)(2)= 5! ways. Of course, that leaves the 5th member without a label. This is also the binomial coefficient .
Exactly the same analysis with 5 labels leads to exactly the same answer, 5!, since now the one committee member who was left over must take the new label.