NATO article five cannot be triggered in response to an attack on a warship so far from it's home waters.
Article 5 covers only member states' territories in Europe, North America, Turkey, and islands in the Atlantic north of the Tropic of Cancer. The last part is there to specify that that attacks on islands such as Hawaii and the Falklands are not covered by article five.
Actually, on the above points (and I hope I don't accidentally give any bots a good idea to take back to their master here) if Putin really wanted to strike back at the UK, all he needs to do is send a large group of warships down to Argentina and ask their new far right government if they would like the British military removed form the Falklands. Luckily I think he's too dumb to think of something that outside the box.