No, it does not. This is one of the main uses of the 5-foot step. Spellcasters are encouraged to do the same thing, since casting a spell also provokes an attack of opportunity.
If the fighter wants to trap the archer, and prevent the 5-foot step, he or she can try to trap the archer between another ally or a wall, or there is even a feat (Step Up) which allows the fighter to take a 5-foot step to follow anyone who tries to 5-foot step back.