Negative Mitzvah 144
It is forbidden for a Priest to eat the first-born sacrifice outside of Jerusalem
Deuteronomy 12:17 "You may not eat within your gates...the first- born of your herds or flocks"
The first-born animals must be redeemed or offered as sacrifices in the Beit Hamikdash (See positive Mitzvah 79).
The priest is entitled to portions of the meat that are not burnt.
A non-priest is not given a portion of this sacrifice.
This Negative Mitzvah applies only to a "perfect" first born animal, one that has no blemishes and is fit to be sacrificed.
This Negative Mitzvah contains two distinct laws.
The first is that a priest may not eat his portion of this first-born sacrifice outside of Jerusalem. The second is that a non-priest is forbidden to eat any of this meat at all.
Negative Mitzvah 108
We are forbidden to redeem first-born animals
Numbers 18:17 "But the first-born of an ox, or the first-born of a sheep, or the first-born of a goat you shall not redeem; they are holy"
At the time of the Exodus from Egypt, HaShem declared that all first-born male children and animals will be sacred to Him.
First-born male children may be "redeemed" in a special procedure called "Pidyon HaBen" (see Positive Mitzvot 79-80).
However, first-born oxen, sheep or goats are considered holy and must be offered as sacrifices. We are forbidden to redeem these first-born animals.