From Aceshowbiz.com:
The first one gives an extended look at how Jack Sparrow is assigned by King George II to find the Fountain of Youth. Jack is dragged into a room by soldiers and is shackled to a chair in front of a table which has a bunch of food with a plate full of creme puffs on it. He tries to get one and kicks the table, but the creme puff flies into the air and gets stuck on a chandelier above him. At the same time, King George II and several men who are dressed in regal uniforms enter the room.
Jack denies his true identity in front of the king at first before he finally admits that he is indeed Jack Sparrow. They talk about the Fountain of Youth, but Jack is making so much noise motioning with his hands still in chains so the king demands that he be unshackled to stop all that noise.
The king says he has a ship and a captain ready for the voyage and it turns out that the man who arranges it is Captain Hector Barbossa. Jack asks Barbossa what happened to the Black Pearl and he's told that he lost it at the same time he lost his leg. Jack then jumps over the table to get at his old arch-nemesis.
In the second clip, Jack is on Blackbeard's ship, the Queen Anne's Revenge. On the deck, Jack talks about staging a mutiny on Blackbeard. Jack tells the crew they will surely die in Blackbeard's quest to find the fountain. As they all stream out, Jack sees Angelica sleeping so he lies down next to her, and she groggily says that if she's dreaming he would keep the sword and the boots on, so he says, "You're dreaming." Angelica angrily kicks him out.
Jack then heads onto deck where a huge sword fight is happening between Jack's men and creepy undead pirates who can't be killed and Jack heads to Blackbeard's quarters to throw the mutiny. When Blackbeard comes out, he motions with his sword and the rigging starts to come to life and grabs all of Jack's men, leaving Jack himself hanging upside down in front of Blackbeard. Jack says, "I want to report a mutiny."
The other is set in an island where Jack makes his way through the jungle before he arrives at a sharp cliff and makes a joke about it not being the right way. Blackbeard, Angelica and others follow behind him and Blackbeard asks someone to jump into the water below and get to the other side. He proposes Jack's name for the task, but Angelica insists she can do it. Blackbeard tells his daughter that if she wants to die, he will just shoot her himself. As Jack seemingly surprises at that statement, Blackbeard takes the challenge involving several empty and filled pistols. Jack picks one which Blackbeard points to Angelica.
After the game is played out, they are back to Jack being the one who will jump, so Jack asks a man who looks like a zombie whether he would survive jumping off the cliff. The man throws a voodoo doll that looks like Jack over the side as Jack screams. When he is told he would indeed survive, Jack jumps over the cliff himself.
Pirates Of The Caribbean: On Stranger Tides hits theaters May 20th, right around the corner!