Charles Ellicott Commentary Ezra 3:5

"and afterward the continual burnt-offering, and [the offerings] of the new moons, and of all the set feasts of Jehovah that were consecrated, and of every one that willingly offered a freewill-offering unto Jehovah." — Ezra 3:5 (ASV)

Both of the new moons. — And of the new moons. The whole verse is general and anticipatory. The new moons, the three feasts, and the constant presentation of freewill offerings, added to the daily sacrifice, made up the essentials of ritual; all of these were, like the arrangements in the Book of Leviticus, established before the Temple was built and afterwards observed.