.
From the context, there is one-to-one correspondence between students and drinks.
So, 30 students each have 1 drink, that are of one of 5 kinds.
Hence, there are 5 groups of 6 students each (6 = 30/5), so that every 6 students inside each of 5 groups have the same drink.
ANSWER to the problem's question is 6 people.
Solved.