Disclaimer: I haven't seen the last film yet.
The first three films form the trilogy of Jack, Elizabeth, and Will, which culminates in Will being turned into the captain of the Flying Dutchman. Also, at the end of the third film, Barbossa steals the Pearl (again), while Jack is left with a map to the Fountain of Youth.
Neither Will nor Elizabeth are present in the 4th film; it picks up approximately where the third one left, with Jack looking for a ship to sail to the Fountain and finding his old crush, Angelica, and her dad - Captain Blackbeard.
The whole affair is irrelevant to the main story, except for the fact that we also see Captain Barbossa, who has lost the Black Pearl in a battle with Blackbeard; Barbossa is now a privateer in King's Navy - he sails in the name of the King to the Fountain, but secretly his real goal is to avenge the Pearl and his lost leg.
Long story short, at the end of the fourth film Jack is left with the Pearl which now looks like this:
Jack is last seen with Gibbs describing (very vaguely) a plan to get the Pearl out of the bottle, and Barbossa is left with Blackbeard's ship, Queen Anne's Revenge.
According to the 5th film's Wikia page, none of the characters introduced in the 4th film make an appearance; however, both Will and Elizabeth return, and since (spoiler from the 5th film!)
Henry's family name is Turner, we can expect some family drama.
TL; DR, or things that are most important:
The epilogue of Pirates of the Carribean: At World's End (the 3rd film), where Will is the Captain of the Flying Dutchman, and has a son with Elizabeth.
The ending of Pirates of the Carribean: On Stranger Tides (the 4th film), Barbossa becomes the captain of _Queen Anne's Revenge:
and where Black Pearl is in a bottle.