I just finished listening to a podcast that dealt with the Falklands war. They spoke about Britain getting the UN Security Council approval, they also spoke about trying to get the US support.
Why didn't (couldn't?) Britain invoke article 5 of the NATO treaty to push the US for help?
There is always more to say, but an answer to this same question appeared here a few months ago. You might like to check that out while you wait for fresh responses to your question.
Why didn't Argentina's invasion of the Falklands trigger NATO's Article 5?, with u/jbdyer