Is FASTI a Wordle Word?

Yes. FASTI is a valid Wordle word.

It is not on the Wordle answer list, so it is unlikely to be a daily answer.

What does FASTI mean?

The calendar, which gave the days for festivals, courts, etc., corresponding to a modern almanac. They were generally engraved on stone, e.g. marble
Records or registers of important events (outside the dominion of Ancient Rome)

Definition from Wiktionary, available under the CC BY-SA license.

Starter word rating: AverageIn the top 30% of all valid Wordle words for testing common letters.
Vowels: A, I
Unique letters: 5 of 5
Common letters: A, T, I

Letter ratings use how often each letter appears in Wordle answers.

Tap its tiles to the colours Wordle showed, and the Wordle Solver lists every word that still fits, with the best next guess.