The first law forbids murder - the ultimate sin against another human being. There is no interpersonal sin comparable to the physical destruction of another person.
Adultery, the second commandment, is an infringement less direct in its assault on another. Torah law states that an adulterous married woman is forbidden to once again relate to her husband. Man is half of a whole. He is unified only when he is together with his spouse. An act which forbids a Man's wife to him - is an act that assaults his essence, by undoing his completion. Thus, this sin is mentioned second.
The third commandment forbids theft. Theft, the assault on another being's property, is more indirect. One's possession is not one's essence. It is, however, something that relates strongly to that essence. As it is more distant from the person's essence than the first two commandments, it is mentioned third.
The fourth commandment forbids false testimony that will damage another person.(14) To damage another person is to steal from him. False testimony, however, is a more indirect act than thievery itself. Thus it is mentioned fourth.
The fifth commandment forbids coveting the belongings of another. Wanting what belongs to another does not hurt that other person. Yet it does damage that person within ourselves, by affecting our feelings towards that person.
This is an affront to something so distant from the essence of another human being. And yet: even this distant infraction represents a break in the moral borders G-d commanded us to remain within - and is, subsequently, forbidden!
14 even when it is not in G-d's name.