Compare the main characters of books 5 and 10 of The Odyssey. What are the similarities? What are the differences?

Books 5 and 10 center around Odysseus, unlike books 1–4, which focus on his son, Telemachus. In this respect, books 5 and 10 actually follow the same main character. Circe and Calypso, however, are central characters in Books 10 and 5 respectively, not only because the two are central personalities in those two chapters, but more importantly because they they do seem to serve as mirrors to one another, fulfilling comparable roles within the poem's narrative structure.
Circe and Calypso are similar in a number of respects. They are both minor goddesses, they both reside on an island far removed from civilization, and they both create lengthy delays in Odysseus's voyage back to Ithaca before helping and preparing him for the next stage in his voyage. Even in their descriptors (The Odyssey, having originally been passed down orally, is filled with various mnemonic devices to aid memorization and recitation) the two overlap. Calypso is occasionally referred to as “the nymph with lovely braids” (see Fagles, Book 5, lines 34 and 63), a description she shares with Circe: “We reached the Aeaean islands next, the home of Circe the nymph with lovely braids” (Fagles, translation, Book 10, lines 148–149). Both are associated with animals—Circe more famously, given her powers of enchantment, but Calypso's cave is explicitly described as being a gathering place of all manner of birds and plants and flowers (Book 5, lines 71–81). It's a recurring theme in Greek mythology and heroic myth—the conflict between civilization and nature (and the conquest of the one over the other). With both Calypso and Circe, we see personalities who seem to be suspended somewhere between the two—they both have servants, and they both have the trappings of civilization (Circe, for example, is described as residing in a palace), but they're also apart from it, isolated as they are on their islands far removed from human interaction. So the similarities are striking—to a degree, they do seem like mirror images of one another.
That being said, there are differences between them too. For all that Circe arrives later in the narrative, her encounter with Odysseus is actually set earlier in the chronology (it should be remembered, much of The Odyssey is Odysseus himself telling his story to the Phaeacians). From that perspective, Calypso is actually one of the last encounters he has on his way back to Ithaca. When he encounters Circe, he still has many of his followers behind him, followers he is ultimately responsible for, whereas by the time Calypso enters the picture, Odysseus is the only survivor that remains, found by Calypso adrift at sea. This is probably the most obvious difference between the two nymphs: Circe is introduced as a malicious force that Odysseus needs to conquer. She uses magic to transform humans into animals, and she turns that sorcery against Odysseus's own people. With the aid of Hermes (who will also arrive later to release him from Calypso's keeping—yet another parallel between the two nymphs), Odysseus is able to overcome Circe's magic, but it is Odysseus himself who must forcibly overcome her before the nymph will grant him aid. Calypso, it must be said, is herself antagonistic (let's not forget, she does entrap him unwilling on her island, intending to make him her husband), but the nature of that antagonism is changed—Circe is an opponent he must overcome and conquer, a malicious force converted into an ally, whereas Calypso is an opponent he can only endure.
This response was written with reference to the Penguin Edition of The Odyssey, as translated by Robert Fagles. See: Homer, The Odyssey. Translated by Robert Fagles. New York: Viking Penguin, 1996.