Argentina undoubtedly committed an act of aggression, and probably would have backed down immediately if faced with the prospect of a NATO alliance against it.
The exact text of Article 5 as found here
The Parties agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all and consequently they agree that, if such an armed attack occurs, each of them, in exercise of the right of individual or collective self-defence recognised by Article 51 of the Charter of the United Nations, will assist the Party or Parties so attacked by taking forthwith, individually and in concert with the other Parties, such action as it deems necessary, including the use of armed force, to restore and maintain the security of the North Atlantic area. Any such armed attack and all measures taken as a result thereof shall immediately be reported to the Security Council. Such measures shall be terminated when the Security Council has taken the measures necessary to restore and maintain international peace and security.
Article 6 further specifies that Article 5 is limited to attacks
The Falklands are obviously not in Europe or North America and are located south of the Tropic of Cancer, thus outside the territories covered by Article 5.
Because article 5 only covers events happening in Europe or North America
Argentina it's probably the southernmost country on Earth, and the islands are right next to it so it would be out of NATO's "jurisdiction".
However I found that Argentina is a major non-NATO ally (MNNA) of the United States. Don't know how that would interfere with Article 5 though.