John Gill Commentary Ezra 5:13

"But in the first year of Cyrus king of Babylon, Cyrus the king made a decree to build this house of God." — Ezra 5:13 (ASV)

But in the first year of Cyrus the king of Babylon
That is, the first year he was king of Babylon, having taken it, otherwise he was king of Persia many years before:

the same King Cyrus made a decree to build this house of God ;
see (Ezra 1:1–4) .