Gemara

Years do not disqualify a Parah Adumah (red heifer), but a Mum (blemish) does. Years disqualify an Eglah Arufah (a calf beheaded for atonement when a murdered body is found; above two or three is Pasul), all the more some a Mum should disqualify it!

Suggestion: A Mum does not disqualify an Eglah Arufah, but work does. A Mum disqualifies Korbanos, all the more so work should disqualify them!

Objection: This Kal va'Chomer is invalid! There is a stringency of an Eglah: age disqualifies it. We cannot learn to Korbanos!

Answer: Some Korbanos also are disqualified by age. The Kal va'Chomer would teach about them (if not for a verse teaching that work does not disqualify them).

Yoma 65a (Beraisa - R. Yehudah): If the bull or goat of Yom Kipur was lost and a replacement was separated, the extra animal must die.

65b: Question: Granted, we decree not to offer the goat the next year, lest we offer a Chatas more than a year old. Why can't we offer the bull the next year?

Answer: We decree lest, in a similar case, we use the goat the next year.

Bechoros 41a (Mishnah): An old, sick, or putrid Korban may not be slaughtered in or outside the Mikdash:

(Beraisa): The exclusions "Min ha'Tzon... Min ha'Kesavim Oh Min ha'Izim" disqualify to the Mizbe'ach an old, sick, or putrid animal.

Had the Torah excluded only an old animal, we would allow a sick animal, for it can heal. Had it excluded only a sick animal, we would allow an old animal, for it is normal to grow old. Had it excluded only these two, which are weak, we would allow a putrid animal. Therefore, all three verses are needed:

Menachos 91b: The Torah specified different Nesachim (accompanying offerings) for sheep in their first and second years. "La'Ayil ha'Echad" teaches that we do not distinguish between the second and third years.

Mishnah (Parah 1:1): R. Eliezer says, an Eglah (Arufah) must be a yearling and a Parah (Adumah) must be two years old;

Chachamim say, an Eglah is two years old, and a Parah is three or four.

R. Meir says, a Parah can even be five years old.

An old Parah is Kosher, but we do not delay it, lest it grow black hairs and become Pasul.

(Mishnah 2 - R. Yosi ha'Glili): Parim are two years old - "Par Sheni Ben Bakar";

Chachamim say, they may even be three years old;

R. Meir says, they may even be four or five years old.

Rishonim

Rambam (Hilchos Ma'aseh ha'Korbanos 1:11): We offer cattle until three full years from day to day, and Tzon (sheep and goats) until two full years. More than this is old, and we do not offer it.

Rambam (Hilchos Bi'as Mikdash 7:1,12): The following Mumim disqualify Kohanim and Korbanos... he is so old that he shakes when he walks.

Rambam (Hilchos Isurei Mizbe'ach 2:6): An old animal may not be offered, but it may not be redeemed until it gets another Mum.

Radvaz: The Rambam already taught that an old animal is Pasul in Hilchos Bi'as Makdish. He repeated it to teach that one may not redeem it.

Mishneh l'Melech: Sotah 46a says that age does not disqualify Korbanos It is clear from Bechoros 41a that an old animal is Pasul mid'Oraisa! This is like the Pesul of an old Kohen, i.e. his strength waned. It does not depend on years. In Hilchos Ma'aseh ha'Korbanos, the Rambam says 'more than this is old, we do not offer it.' This is mid'Rabanan, because it is dishonorable. Menachos 91a explicitly says that a three-year old sheep can be offered!

Tosfos Yoma (65b DH mi'Shum): Why is it only a decree not to offer the bull the next year, lest we offer an old goat? We should decree lest we offer a bull above three! Perhaps we may not offer such a bull, but it may graze until it gets a Mum, and we ask why it must die! Alternatively, we ask how we can answer for R. Meir, who allows bulls of any age.

Turei Even (Rosh Hashanah 10a DH Gam): An old bull is disqualified due to weakness. This is evident, so one would not err and offer it. A goat past one year is disqualified. One could err about this.

Mishnah Acharonah (Parah 1:1 DH u'Parah): Chachamim allow buying a three year old Parah Adumah to slaughter it later, or a four-year old to slaughter it immediately. We do not delay longer, lest it grow black hairs. R. Meir allows waiting until five years. All agree that b'Di'eved, age does not disqualify it (Sotah 46a). Alternatively, R. Meir explains Chachamim. The Bartenura holds like this, for he rules like R. Meir. In Mishnah 1:2, Tana'im argue about whether Parim may be up to two, three or five years old. This is when the Torah specified Ben Bakar. What is Tosfos' source to say that R. Meir allows bulls above five?

Question (Mishneh l'Melech): Tosfos says that perhaps a bull above three need not die. They hold that the Pesul is mid'Oraisa. The Gemara says that age does not disqualify Korbanos (Sotah 46a)!

Answer #1 (Mishnah Acharonah): Perhaps the Gemara refers to rams.

Answer #2 (Rashash Chulin 115a DH Choresh): The age limit for Parim is only when the Torah specified Parim, e.g. for Musafim, Par Helam Davar... When it says only "Bakar", there is no limit.

Rashi (in Shitah Mekubetzes Kesuvos 75a DH v'Zeh Lashon Rashi): I am unsure when an animal is considered old. For a person, it is when he shakes.

Rambam (Hilchos Parah Adumah 1:1): The Mitzvah is for Parah Adumah to be three or four years old. If it was Zaken (older than this) it is Kosher, but we do not delay it, lest it grow black hairs and become Pasul.

Mishneh l'Melech (DH Mitzvas): In Hilchos Ma'aseh ha'Korbanos, the Rambam says that above three is Zaken! The Shi'urim for Par and Parah are different. A Par must be at least two, and a Parah must be at least three. Each is called Zaken two years after it became Kosher. Further, Parah is Kodshei Bedek ha'Bayis. It is not a Korban, therefore we needed a verse to teach that a Mum disqualifies it. A verse disqualifies Zaken for Korbanos. We have no source to disqualify Zaken for Parah. It seems that also a putrid or sick Parah should be Kosher, for these are disqualified for Korbanos from the same verse that disqualifies Zaken. However, we disqualify a Tereifah for Parah (Chulin 11) because it is called Chatas, and the Rambam (1:7) says that any Pesul for Korbanos, e.g. it was traded for a dog, disqualifies Parah. Why is Zaken different? The Torah disqualifies Zaken only due to weakness. The Pesul due to years is only mid'Rabanan. Perhaps it is 'Pasul' only due to honor. Only Pesulim mid'Oraisa disqualify Kodshei Bedek ha'Bayis.