Φοῖβε ἄναξ, ὅτε μέν σε θεὰ τέκε πότνια Λητώ (5)
φοίνικος ῥαδινῆς χερσὶν ἐφαψαμένη,
ἀθανάτων κάλλιστον, ἐπὶ τροχοειδέϊ λίμνῃ,
πᾶσα μὲν ἐπλήσθη Δῆλος ἀπειρεσίη
ὀδμῆς ἀμβροσίης, ἐγέλασσε δὲ γαῖα πελώρη,
γήθησεν δὲ βαθὺς πόντος ἁλὸς πολιῆς. (10)
5. Φοῖβος as an adjective, bring, shining; an epithet of Apollo, Phoebus. ἄναξ ἄνακτος ὁ king, leader. τίκτω, τέξομαι, ἔτεκον beget, bring forth; here the aorist without augment. πότνια ἡ lady, queen used mostly to address noblewomen and goddesses. Λητώ Leto, mother of Apollo.
6. φοῖνιξ ικος ὁ purple, red; as an adjective; palm tree as a noun (that's the meaning here). Apollo and his sister Artemis were born under a palm tree, near the round lake of Delos. ῥαδινός ή όν slender, slim; tender apparently the palm tree had a male and female form; this adjective agrees with φοίνικος fem.gen.pl. χείρ χειρός ἡ hand; here the dative of means, "with (her) hand." ἐφ‐άπτω make fast; in middle, hold, grasp, reach with genitive.
7. ἀθάνατος ον undying, immortal.
κάλλιστος η ον superlative of καλός best, fairest.
8. πίμπλημι, πλήσω, ἔπλησα, πέπληκα, ἐπλήσθην fill; passive become filled of; have enough of with genitive. Δῆλος ἡ Delos, birthplace of Apollo and Artemis. ἀπειρέσιος η ον boundless, countless, immense. It's not exactly clear how an island in the Aegean may be considered boundless. Tyler suggests perhaps it should be considered almost adverbial, "all of Delos was completely filled..."
9. ὀδμή ἡ = Attic ὀσμή, odor, scent. ἀμβρόσιος η ον sweet smelling, fragrant; this recalls also ἀμβροσίη , the food of the gods which makes them immortal, and which was apparently used also as a perfume. γελάω , 3.sg. aorist ἐγέλασσε laugh. γαῖα ἡ a poetic word for γῆ, earth, land. πέλωρος (η) ον monstrous, huge, gigantic.
10. γηθέω rejoice. βαθύς εῖα ύ deep, thick. πόντος ὁ sea; specifically, the open sea as a pathway over water. The set Homeric phrase πόντος ἁλός means "the deep of the sea" or "ocean." ἅλς ἁλός when masculine, means salt when feminine, sea. πολιός (ή) όν grey, grey-ish; grizzled; "the grey sea" is a common Homeric phrase.
The last phrase means something like "the deep depths of the grey sea."