1. He finished the project in five days.

2. He finished the project within five days.
3. He finished the project after five days.
[Does #1 mean #2? What about #3? What are the differences among them?]

He finished the project after five days? In six days, in ten days, a year later? That means something far different than #1 and #2, which mean, essentially, the same. One is more precise, meaning five days, no more, no less. Number two means less than five days (maybe four and a half?).