Tractate Bekhorot - Chapter 9 - Mishnah 6 בכורות פרק ט׳ משנה ו׳

All those born from the first of Tishrei until the twenty-ninth of Elul combine [for matters of tithing]. Five lambs born before Rosh Hashanah and five born after Rosh Hashanah do not combine. But five lambs born before the period [of tithing] and five after the period [of tithing] do combine [for tithing]. If so, why did they speak of three periods for the tithe of cattle? Until the arrival of the [tithing] period it is permitted to sell and slaughter [the animals], but when the period has arrived he must not kill, but if he killed, he is exempt.