If no one shares an office, in how many ways can 3 people be assigned to 5 different offices? (Each person gets exactly one office).
Here's my (probably not correct) take on this problem. Choose 3 offices out of 5 to be the ones that are assigned to people. Now count how many ways there are to order that; that should be your answer.
Or, another way, first person has 5 choices. How many does the second have?