Books 5-8 constitute the second of the six 4-book units into the Odyssey can be readily divided. Books 1-4 focus mainly on Telemachos, and Books 5-8 on Odysseus' experiences among the Phaiacians (or Phaiakians or Phaiakes) and the events (in Book 5) leading up to this.
At the beginning of book 5, there is a second council of the gods, and Hermes is sent to Kalypso to convey the gods' will that Odysseus be allowed to return home. Kalypso reluctantly agrees - even though she tries to persuade Odysseus to remain with her by making him immortal.
Off and on through Books 6-8, Athena intervenes in various ways on Odysseus' behalf.
At the beginning of book 6, she appears in a dream to Nausikaa, daughter of Alkinoos and Arete, King and Queen of the Phaiacians. In the dream, Athena suggests that Nausikaa take the family laundry down to the seashore to wash and dry. (This will involve Odysseus, inasmuch as the boat with which he had left Kalypso's island has been wrecked by Poseidon, and he has been cast ashore near where Nausikaa will take the laundry.)
Next, near the beginning of Book 7, Athena appears, disguised as a young girl, and leads Odysseus to Alkinoos' palace. Then, near the beginning of Book 8, Athena appears, again disguised - this time as Alkinoos' herald - to urge the Phaiacians to come to an assembly and hear about the stranger (whom we know to be Odysseus) who has just appeared among them. Finally, when Odysseus competes in discus-throwing with the Phaiacians, Athena appears again, disguised as a nameless Phaiacian, to compliment Odysseus on the excellence of his discus throw.
Another important sequence of events in Book 8 is formed by the three songs of the bard Demodokos.
Soon after Athena's initial appearance in Book 8, Demodokos sings about "the quarrel of Odysseus and Achilles". There are various scholarly theories about the exact relevance of this, but in a general way it would seem to suggest the overall theme of the Iliad - a quarrel - and so complement the song of Phemios in Odyssey, Book 1. (Phemios' song was described as being about the Nostoi - "Returns" - of the Achaians from Troy; hence, it dealt with the same overall sort of thing as the Odyssey itself, viz., Odysseus' return from Troy.)
Demodokos' second song is the famous - or infamous - story of the love affair of Ares and Aphrodite. This is given in full by Harris and Platzner, pp. 211-213 - but outside of its context in the Odyssey. In a way, the "Loves of Ares and Aphrodite" is an excellent example of the immoral divine behavior which Xenophanes complained of as an undesirable feature of Homer's and Hesiod's portrayal of the gods. On the other hand, one could also observe that the eventual outcome of the story is that the adulterous pair, Ares and Aphrodite, are made very uncomfortable by the wronged husband, Hephaistos. In some ways, then, the story parallels, on the divine level, the story of the love affair of Klytemnaistra and Aigisthos, mentioned by Zeus near the very beginning of the Odyssey.
Finally, the third and last of the songs of Demodokos in Book 8 is the story of the wooden horse. Devised by the craftiness of Odysseus, the wooden horse is an excellent example of the importance of Odysseus in the Trojan War, and it can thus serve to fill out the more or less mysterious reference to the quarrel of Odysseus and Achilleus, sung of by Demodokos near the beginning of Book 8. I.e., in some way the quarrel would seem to be one between brawn (Achilles) and brains (Odysseus) - and Odysseus is ultimately the one who is responsible for the capture of Troy.