This Mishnah, Bechoros 8:5, continues with matters of doubt. The case before us: two men and their two wives, and the women give birth in a dark cave. In the morning, it becomes clear that the babies were mixed up, and no one knows which baby belongs to which mother. What is their status regarding the redemption of the firstborn?
The first case - two males:
The two women are married to two different men, and neither of them has given birth previously; therefore, their first child, if a male, requires redemption. In the morning, two male babies were found in the cave. Although they do not know who the mother of each one is, it is known that each child is the firstborn to his mother, and therefore each of them is a firstborn requiring redemption.
Therefore, the law is that each of the two fathers gives five selaim to a kohen. Each of them knows with certainty that a son requiring redemption was born to him here; he does not know which of the two babies is his son, but he knows that one of them is his son, and therefore he redeems him.
One of the sons died within thirty days:
If one of the two sons died within thirty days, once again they do not know which of the two fathers is exempt from the redemption of the firstborn. In this regard, the Mishnah distinguishes between two situations:
They both gave to one kohen: If the two fathers paid five selaim each in advance to a kohen before the end of thirty days - a surprising situation in itself - and stipulated that upon the completion of thirty days, when the obligation of redemption takes effect, the money will serve as the redemption money for the son, they are both permitted to jointly demand a refund of five selaim. After all, ultimately there is only one child here requiring redemption, and the kohen is entitled to only five selaim and not ten, and he must return five.
They gave to two kohanim: If they gave to two different kohanim, neither of the fathers can collect a refund from either of them, as each kohen claims: "How do you know that the son who died is not the one redeemed by your friend?" This refers to a case where it was not specified for whom the kohen is receiving the five selaim.
A male and a female:
If one male and one female were found in the cave, it is clear that there is a firstborn here, as that baby knows about himself that he is a firstborn. However, each of the fathers can claim: "Who says that the firstborn is my son? Perhaps the daughter is my daughter." Therefore, the Mishnah establishes that both fathers are exempt from giving five selaim.
However, the son himself knows his status in relation to his mother: even though he does not know which of the two women is his mother, he knows that both of them gave birth for the first time, and it turns out that for his mother he was the 'peter rechem' (first issue of the womb) and requires redemption. Therefore, even though his father is exempt from paying, it is incumbent upon him to redeem himself once he reaches the age of mitzvos.
Two females with one male or with two males:
If in the morning it is found that the two women married to two different men gave birth, and in the room are two daughters and with them one son or two sons - in both cases the kohen receives nothing. The reason: it is possible that one daughter was born first to this mother and one daughter was born first to the second mother, and there is no firstborn son here at all, as the one son or the two sons were born after their twin sister.
In summary: For two males - each father gives five selaim; if one of them dies within thirty days - if they gave it to one kohen, they receive five selaim back, and if they gave it to two kohanim, they cannot take it back from them. For a male and a female - the fathers are exempt, and the son must redeem himself. For two females with a male or with two males - the kohen gets nothing.