In book 5 of the Odyssey, what is Odysseus doing when he first appears?
Odysseus is first mentioned in Book V by Athena, who describes him as "...lying in great pain in an island where dwells the nymph Calypso, who will not let him go;". Zeus, who is guilted into action by his daughter Athena (who is a partisan of Odysseus) then sends his messenger, the god Hermes, to Calypso's island to free Odysseus. When Hermes first meets Calypso in her house, while she is working at her loom with a golden shuttle, it is noted that Odysseus is not there. "...but Odysseus was not within; he was on the sea-shore as usual, looking out upon the barren ocean with tears in his eyes, groaning and breaking his heart for sorrow." Calypso is not keen on letting Odysseus go, for she is fond of him and planned to make him immortal, but she knows that she must yield to Zeus's orders. Hermes says that she must send Odysseus away, and then the gods' messenger leaves her.
Calypso goes out to the shore, and this is where Odysseus first actually appears.
...Calypso went out to look for Odysseus, for she had heard Zeus' message. She found him sitting upon the beach with his eyes ever filled with tears, and dying of sheer home sickness; for he had got tired of Calypso, and though he was forced to sleep with her in the cave by night, it was she, not he, that would have it so. As for the day time, he spent it on the rocks and on the sea shore, weeping, crying aloud for his despair, and always looking out upon the sea.
So Odysseus, glad to be alive, surely, and happy to have a fling with the goddess for awhile, has grown homesick for Ithaca. Then, as Zeus had decreed that Odysseus was not to leave Calypso's island by means of other men and their ships, nor by the action of a god, Calypso tells Odysseus to make himself a seaworthy raft and leave her island. Odysseus builds his raft, and leaves, provisioned by Calypso. Thus Odysseus ends up on the island of Scheria (by a harrowing adventure of swimming in a magic veil because of another storm from the wrath of the god Poseidon) and it is there, eventually, among the Phaecians, that Odysseus tells the rest of his story up to the point where he came to Calypso's island.