So the new Pirates movie was way better than 3 or 4. It was on par with #1, which I felt was actually a really good movie. It was better than 2, but I liked 2 for the characters and the milieu. 3 just got stupid and overblown and 4 was a bad remake of 2 basically.
To answer the questions, unfortunately it is not a stand-alone movie. There are hints and outright plot points tied directly to all of the other movies. It felt like a wrap-up of the whole franchise really. There is an event at the end that kind of precludes any further "magical" adventures. However, the after credits scene hints at more to come that might be ok or might be really stupid.
I think they can really do good things within this franchise, and frankly it is the only thing I can watch Jonny Depp in anymore. He has become such a caricature of himself it is kind of pathetic, but he is in his element in the Pirates movies. And he does a decent job in this one.
Another decent twist in the Dead Men Tell No Tales was that they made a good guy into the villain, and my family and I are not sure how we feel about that. It made for all sorts of interesting conversation as we talked about the absolutes of good vs evil. More thought provoking than I think the movie-makers intended as they did not play up that aspect very much, but the undertones are there.
All in all I would give it a solid B or even B+. Fun movie, more depth both in character and story, than you might expect and a wholly satisfying ending. Will watch again.