A group of campers is going to occupy 5 campsites at a campground. There are 17 campsites from which to choose. In how many ways can the campsites be chosen?
There are possible ways to choose the campsites.

Step 1 ：This problem is about choosing 5 campsites out of 17 available ones. The order in which the campsites are chosen does not matter, so this is a combination problem.

Step 2 ：The formula for combinations is $C(n,k)=\frac{n!}{k!(n-k)!}$, where n is the total number of items, k is the number of items to choose, and '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：In this case, n = 17 (the total number of campsites) and k = 5 (the number of campsites to be chosen).

Step 4 ：Substituting the values into the formula, we get $C(17,5)=\frac{17!}{5!(17-5)!}$.

Step 5 ：Solving this, we find that there are 6188 ways to choose 5 campsites out of 17.

Step 6 ：Final Answer: The number of ways the campers can choose 5 campsites out of 17 is $\boxed{{\displaystyle 6188}}$.