1. The problem states that a teacher has 5 different pets and 16 volunteers out of 75 students. 2. The teacher will select 5 volunteers to take 1 pet each. 3. We want to find the appropriate values of $n$ and $r$ for the permutation formula $n\text{P}r = \frac{n!}{(n-r)!}$. 4. Here, $n$ represents the total number of volunteers to choose from, which is 16. 5. The value $r$ represents the number of volunteers selected, which is 5. 6. Therefore, the appropriate values are $n=16$ and $r=5$. 7. This means the number of unique ways to distribute pets is $16\text{P}5 = \frac{16!}{(16-5)!} = \frac{16!}{11!}$.