C6 BCE. See generally OCD(4) pp.83-4, under Anaximenes(1).
[1] alpha 1986.
[2] pi 675.
[3] Something is wrong here, either chronologically or textually: the 55th Olympiad was 560-557, the capture of Sardis 546. Adler (addenda) notes Daub's proposal to add oi( de/ before 'during ...', so that the sentence contains two different chronological alternatives. But another approach to the issue is suggested by Diogenes Laertius 2.3, who also synchronized Anaximenes' floruit with the fall of Sardis (and adds that Anaximenes died in the 63rd Olympiad, 528-525). That passage of D.L. is FGrH 244 F66 [66a BNJ], i.e. regarded as coming from Apollodorus of Athens, a polymath of the C2 BCE (OCD4 p.120 s.v. Apollodorus(6)), and indicates that it was Apollodorus who originally synchronised the acme of Anaximenes with the fall of Sardis. See on this Mosshammer (1976) 296, and further in Mosshammer (1979) 276-7 with n.5: 'That Anaximenes' floruit was associated with the fall of Sardis is confirmed, at least obliquely, by the article of the Suda on him. The Suda says that he flourished in the 55th Olympiad (560-557), at the time of the fall of Sardis, when Cyrus of Persian defeated Croesus. The sources of the Suda correctly transmitted the [Apollodoran] synchronism between the acme of Anaximenes and the fall of Sardis, making it clear that the reference is to Cyrus' defeat of Croesus. The sources assigned the wrong date to the synchronism, however, associating Anaximenes with the 55th Olympiad. Olympiad 55 was the universal chronographic date for the accession of Cyrus. The compiler of the Suda's report introduced the date for Cyrus instead of that of Croesus' fall'.