Last Five Bullets

A man, who's been living in hard times, finally gets a break when Curaga, who's known for curing most forms of cancer, offers him a worthwhile job. If he fulfills his duty as a guard to bring part of a cure to them, his daughter will be cured of her incurable disease, however, things go wrong and a sort-of zombie outbreak happens with zombies who can only be killed with fire and the five last bullets he has in a special issued pistol.
Can he survive against hordes of mutating, flesh-eating zombies with only five bullets?