The frame
On the Met's timeline for Egypt, 1000 BCE-1 CE, the Late Period is dated "ca. 712-332 B.C." and comprises Dynasties 25 to 30. According to the timeline, although unified under Dynasties 25, 26 and 28 to 30, Egypt sees considerable turmoil; yet, "somewhat surprisingly", the Late Period is "an extremely fruitful time both conceptually and artistically". The museum's essay on the period, by Marsha Hill and James P. Allen, divides it into the Saite Period, Dynasty 26 (664-525 BCE), the Persian Period, Dynasty 27 (525-404 BCE), and Dynasties 28 to 30 (404-343 BCE); in 343 Egypt fell once again to the Persians, who were defeated in turn by Alexander the Great in 332. Sources 1, 2.
Boundaries and overlaps
At the start of the period two sources from the same museum disagree. The timeline opens it in 712 BCE and counts in it Dynasty 25, which it separately dates, as "Nubian control, Dynasty 25", to ca. 743-664 BCE; the essay is titled "Egypt in the Late Period (ca. 664-332 B.C.)" and does not deal with Dynasty 25: its first section is the Saite Period. Nor does the essay give a single starting year: when the Assyrians withdrew after their final invasion in 664 BCE, Egypt was left in the hands of the Saite kings, "though it was actually only in 656 B.C." that the Saite ruler Psamtik I was able to reassert control over the southern area of the country, dominated by Thebes. Sources 1, 2.
Why no single year decides
The site's navigation uses the timeline's line at 712 BCE so that Egypt's periods follow one sequence, and this page states the essay's 664 explicitly. Neither year decides on its own: 712 is where the timeline opens the period, without tying it, in the text read, to a named event; 664 is, according to the essay, the year of the Assyrian withdrawal; and 656 is the year in which, according to it, Saite control reached the south as well. An object or article from Dynasty 25 or from the beginning of Dynasty 26 is placed on this site by the wording of its own source, not by a single year. Sources 1, 2.
On this site
"Naukratis: a Greek trading settlement in the Delta" reads the essay's sentence that the Greek city-states were allowed to establish a trading settlement in the western Delta, and shows what the sentence does not describe. "Egypt under a Persian satrap: Dynasty 27" deals with rule through a resident governor and with why the period is hard to identify in the material record.