The main conflict of Book 5 is the sea nymph Calypso. After Odysseus landed on her island, she kept him there with her, not allowing him to leave. This book opens with a conversation between Athena, Zeus, and Hermes; Athena is complaining to Zeus about how Odysseus is trapped on the island, so Zeus instructs Hermes to go down to Calypso's island and talk to her. Hermes accepts his given mission and journeys to where Calypso lives. Calypso is pleasant at first because she has no idea what Hermes is there for, but when he tells her that she must release Odysseus because he is not meant to waste his life in exile, she becomes angry. She accuses the god of being jealous of her because she was lying with a mortal man; but despite her protests, Hermes says very briefly that if she does not let Odysseus go, she will be punished by Zeus, and then he leaves. When she goes to tell Odysseus that she will help him leave, he is suspicious at first, but eventually he has a raft and she helps him sail away.
There is another conflict in Book 5, though it is not quite as large: while Odysseus is out on the open sea on the raft Calypso helped him build, Poseidon makes the sea turbulent, trying to kill Odysseus, and it is only with the help of Athena and another sea nymph that Odysseus makes it to the island of the Phaeacians.