If we're quite narrowly just looking at the raw text of Article 5, the answer is fairly simple; the collective response is intended to trigger when an attack is in Europe, North America, or "the Algerian Departments of France" and it quite specifically mentions (in the clarifications of what constitutes an "armed attack") that the Tropic of Cancer is the dividing line. Any NATO member assistance in a military sense (which was provided by one ally, and I'll get to that shortly) would thus be voluntary.
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 ...
Having said all that, there's "soft" implications of Article 5 in play. Britain needed to move a large force in order to wage the war, which meant the country needed to convince NATO that this was an acceptable transfer of forces from Europe. In other words, even though there was no military obligation to join forces, the needed to be at least tacit approval to temporarily change the level of NATO forces. Indeed, this was actually the case, as NATO entirely endorsed Britain's effort.
One of the claimed reasons behind the support is that the war served as a "testing ground" for what would be NATO weapons in a full-on land war in Europe. This was explicitly said after the war, where there was some concern that the loss of two destroyers, two frigates, and other assorted vehicles and personnel had weakened NATO, and the Defense Secretary Michael Heseltine made the argument that
an "assessment of Western defenses as a whole" includes British will and defenses and that
the British learned lessons from the Falklands campaign that will help NATO as a whole.
The ramification was a "soft diplomacy" re-affirmation of Article 5, even if it didn't get officially invoked. If, say, Italy had stepped out of line (they had a large population in Argentina, and would have been the most likely candidate), there would now be the question of would the actual obligation under the treaty really be carried out? History is littered with broken treaties, and international history should be understood not just under the lens of carrying out the literal text of words, but the inherent faith made behind implied promises.
A good example of "text vs. reality" would be Algeria. I did say earlier that Algeria was shoehorned into Article 5. Thus, when France waged their own war, technically speaking the operations took place on NATO-obliged territory, yet there was not a NATO trigger. As the country was constitutionally French, the French government insisted that NATO not be directing the conflict, yet eventually they tried to wheedle material aid. Essentially, France was trying to have a conflict that was both not-NATO and NATO at the same time. Additionally, a fair number of NATO countries didn’t have have a desire to intercede further; Britain, Turkey, and Greece, for instance, didn't want to upset the Egyptians, and the US was skeptical generally and explicitly stated the French "could not have a blank cheque".
This may seem strange if you interpret Article 5 as an absolute trigger on military force, but it really is written more flexibly than that. Signatories take "such action as it deems necessary" to protect the listed area. Considering the US specifically, an actual Article 5 trigger would require approval from Congress; while the Commander in Chief has a broad mandate when it comes to defense of the United States, this does not extend to involving military force in an ally getting attacked.
Hence, Article 5 -- and really, any treaty in history -- has a little more complexity than it might appear, and just because something is or is not written down doesn't mean the reality will match. This was also why there was some aid from the US with the Falklands to Britain; even though there absolutely no obligation, they still provided
... 12.5 million gallons of aviation fuel diverted from U.S. stockpiles, along with hundreds of Sidewinder missiles, airfield matting, thousands of rounds of mortar shells and other equipment ...
and a promise to lend the USS Guam if the British lost any of their carriers (they did not).
Defense Secretary Weinburger was concerned that if Britain was defeated, that it would have a "deterrent quality" to NATO. The aid also reaffirmed friendship and the fact Article 5 would be followed if it were it invoked, as it eventually was in 2001 followed by Britain making the biggest contribution of any European NATO country to the war in Afghanistan.
...
Kaplan, P. L., Kaplan, L. S. (2004). NATO Divided, NATO United: The Evolution of an Alliance. United Kingdom: Praeger.
Stransky, S. G. (2011). Re-Examining the Falkland Islands War: The Necessity for Multi-Level Deterrence in Preventing Wars of Aggression. Ga. J. Int'l & Comp. L., 40, 473.
Thomas, M. (2000). The Algerian Conflict—a Cold War Front Line?. In The French North African Crisis (pp. 158-178). Palgrave Macmillan, London.