Will a MacBook Air 13 with M5 processor be released?

Nope. Apple has not made any announcement about M5 MacBook Airs.

Since the M4 MacBook Airs were just released in March of this year, it's unlikely an M5 MacBook Air would be released before March of next year.

No. We are not Apple. Rumor and speculation are prohibited by the Apple Support Community Terms of Use.