What is the meaning of the Panca-maha-yajna mentioned in BG 3.12 purport?
“For ordinary men, at least five yajïas, known as Panca-maha-yajna, are necessary.” - Bhagavad Gita 3.12 purport
Q: What are these five primary yajnas?
A: As the above-quoted purport indicates, they are karma-kanda rituals which householders who are not vaisnavas are obliged to perform. What follows are two different lists of these five yajnas. The source for the first list I do not know but I have no reason to challenge; Manu-samhita, the second, is a known standard authoritative source, however the translator needs a qualified editor.
After performing his midday sandhya prayers and Deity worship, the grhastha should perform five yajnas before taking his main meal of the day to absolve himself of all debts. These yajnas are as follows:
deva yajna: homa to the Deity
brahman yajna: study of the Veda
pitr yajna: offerings to the ancestors
bhuta yajna: offerings to other entities
nr yajna: offerings to men, in the form of feeding guests
Deva Yajna: Some people make offerings of Visnu prasada anna in the fire to the vaisvadevas as deva yajna. Others claim that the puja and sandhya ruts cover all obligations to deva yajna.
Brahma Yajna: This is accomplished if one studies the four Vedas. However the tradition has arisen that one recites the first four verses of each Veda after the noon sandhya as brahma yajna, whether one actually studies the Vedas or not
There are five kinds of domestic sacrifices performed by Vedic householders (grhasthas). They are mentioned in Bhagavad Gita 3.12 purport etc. Manu-samhita (3.67-74 and further) explains:
67. With the sacred fire, kindled at the wedding, a householder shall perform according to the law the domestic ceremonies and the five (great) sacrifices, and (with that) he shall daily cook his food.
68. A householder has five slaughter-houses (as it were, viz.) the hearth, the grinding-stone, the broom, the pestle and mortar, the water-vessel, by using which he is bound (with the fetters of sin).
69. In order to successively expiate (the offenses committed by means) of all these (five) the great sages have prescribed for householders the daily (performance of the five) great sacrifices.
70. Teaching (and studying) is the sacrifice (offered) to Brahman, the (offerings of water and food called) Tarpana the sacrifice to the manes, the burnt oblation the sacrifice offered to the gods, the Bali offering that offered to the Bhutas, and the hospitable reception of guests the offering to men.
71. He who neglects not these five great sacrifices, while he is able (to perform them), is not tainted by the sins (committed) in the five places of slaughter, though he constantly lives in the (order of) house (-holders).
72. But he who does not feed these five, the gods, his guests, those whom he is bound to maintain, the manes, and himself, lives not, though he breathes.
73. They call (these) five sacrifices also, Ahuta, Huta, Prahuta, Brahmya-huta, and Prasita.
74. Ahuta (not offered in the fire) is the muttering (of Vedic texts), Huta the burnt oblation (offered to the gods), Prahuta (offered by scattering it on the ground) the Bali offering given to the Bhutas, Brahmya-huta (offered in the digestive fire of Brahmanas), the respectful reception of Brahmana (guests), and Prasita (eaten) the (daily oblation to the manes, called) Tarpana.