The "fifth" Veda Samhita explained by Srila Prabhupada is the Mahābhārata.

Bhagavad-gītā As It Is, is the fifth Veda, which is part of the Mahābhārata.

Why did Lord Krsna give Vedic wisdom to the human race?

Srila Prabhupada - "All material activities involve actions and reactions in the three modes of material nature. They are meant for fruitive results, which cause bondage in the material world.

The Vedas deal mostly with fruitive activities to gradually elevate the general public from the field of sense gratification to a position on the transcendental plane.

All the living entities who are in the material world are struggling very hard for existence.

For them the Lord, after creation of the material world, gave the Vedic wisdom advising how to live and get rid of the material entanglement.

When the activities for sense gratification, namely the karma-kāṇḍa chapter, are finished, then the chance for spiritual realization is offered in the form of the Upaniṣads, which are part of different Vedas, as the Bhagavad-gītā is a part of the fifth Veda, namely the Mahābhārata.

The Upaniṣads mark the beginning of transcendental life." (Bhagavad-Gita As It Is 2.45, Purport)

Srila Prabhupada - "The Vedas deal mainly with the subject of the three modes of material nature. O Arjuna, become transcendental to these three modes and be free from all dualities and from all anxieties for gain and safety, and be established in the self.

All material activities involve actions and reactions in the three modes of material nature. They are meant for fruitive results, which cause bondage in the material world. 

The Vedas deal mostly with fruitive activities to gradually elevate the general public from the field of sense gratification to a position on the transcendental plane. 

Arjuna, as a student and friend of Lord Kṛṣṇa, is advised to raise himself to the transcendental position of Vedānta philosophy where, in the beginning, there is brahma-jijñāsā, or questions on the supreme transcendence. 

All the living entities who are in the material world are struggling very hard for existence. For them the Lord, after creation of the material world, gave the Vedic wisdom advising how to live and get rid of the material entanglement. 

When the activities for sense gratification, namely the karma-kāṇḍa chapter, are finished, then the chance for spiritual realization is offered in the form of the Upaniṣads, which are part of different Vedas, as the Bhagavad-gītā is a part of the fifth Veda, namely the Mahābhārata. 

The Upaniṣads mark the beginning of transcendental life". (Bhagavad-Gita As It Is Chapter 2 text 45, Translation and Purport)

Srila Prabhupada - "Above the four Vedas, namely Ṛg, Yajur, Sāma, and Atharva, there are the Purāṇas, the Mahābhārata, Saṁhitās, etc., which are known as the fifth Veda. 

Śrī Vyāsadeva and his many disciples were all historical personalities, and they were very kind and sympathetic toward the fallen souls of this age of Kali. 

As such, the Purāṇas and Mahābhārata were made from related historical facts which explained the teaching of the four Vedas. 

There is no point in doubting the authority of the Purāṇas and Mahābhārata as parts and parcels of the Vedas. 

In the Chāndogya Upaniṣad (7.1.4), the Purāṇas and Mahābhārata, generally known as histories, are mentioned as the fifth Veda. 

According to Śrīla Jīva Gosvāmī, that is the way of ascertaining the respective values of the revealed scriptures". (Srimad Bhagavatam Canto 1 Chapter 4 text 19, Purport)

SB 1.4.20, Translation - "The four divisions of the original sources of knowledge (the Vedas) were made separately. But the historical facts and authentic stories mentioned in the Purāṇas are called the fifth Veda".

SB 3.12.39, Translation - "Then he created the fifth Veda—the Purāṇas and the histories—from all his mouths, since he could see all the past, present and future".

Srila Prabhupada - "There are histories of particular countries and nations and of the world, but the Purāṇas are the histories of the universe, not only in one millennium, but in many kalpas. 

Brahmā has knowledge of those historical facts, and therefore all the purāṇas are histories. 

As originally composed by Brahmā, they are part of the Vedas and are called the fifth Veda". (SB 3.12.39, Purport)

Srila Prabhupada - "Śrīla Vyāsadeva is called Mahāmuni. He is also known as Vedavyāsa because he has compiled so many śāstras. 

He has divided the Vedas into four divisions—

Sāma, 

Ṛg, 

Yajur, 

Atharva. 

He has expanded the Vedas into eighteen Purāṇas and has summarized Vedic knowledge in the Vedānta-sūtra. 

He also compiled the Mahābhārata, which is accepted as the fifth Veda. 

The Bhagavad-gītā is contained within the Mahābhārata. Therefore the Bhagavad-gītā is also Vedic literature (smṛti). 

Some of the Vedic literatures are called śrutis, and some are called smṛtis. 

Śrīla Rūpa Gosvāmī recommends in the Bhakti-rasāmṛta-sindhu (1.2.101):

śruti-smṛti-purāṇādi-pañcarātra-vidhiṁ vinā

aikāntikī harer bhaktir utpātāyaiva kalpate

(Brs. 1.2.101)

Unless one refers to śāstra (śruti, smṛti, purāṇa and so on), one's spiritual activity simply disturbs society". (Sri Caitanya-caritamrta Madhya 20.353, Purport)

Srila Prabhupada - "We understand that with the breathing of the Supreme Personality of Godhead there issued forth the four Vedas, namely the 

Ṛg Veda, 

Yajur Veda, 

Sāma Veda,

Atharva Veda.

And also the histories like the Mahābhārata and all the Purāṇas, which are considered to be the history of the world. 

The Vedic histories like the Purāṇas and Mahābhārata are called the fifth Veda.

The twenty-eight verses of the Veda-stuti are to be considered the essence of all Vedic knowledge. 

The four Kumāras and all other authorized sages know perfectly that devotional service in Kṛṣṇa consciousness is the essence of all Vedic literature, and they preach this on different planets, traveling in outer space. 

It is stated herein that such sages, including Nārada Muni, hardly ever travel on land; they perpetually travel in space". (Krsna Book 87)

Srila Prabhupada - "Therefore the same thing. The Vedic knowledge was described in the Mahābhārata. Because it is history. 

Everyone is interested to read history. So through history, the Vedic knowledge was imparted. Therefore, Mahābhārata is called the fifth Vedas. 

There are five Vedas, 

Sama, 

Yajur, 

Ṛk, 

Atharva. 

And Mahābhārata is fifth Veda. 

They are meant for this stri, śūdra, dvija-bandhu. So Bhagavad-gītā is within the Mahābhārata. 

So actually it was meant for the less intelligent class of men. But, at the present moment, the highest intelligent class of men cannot understand. 

Just see the difference. Formerly, 5000 years, this was meant for the less intelligent class of men, and we have deteriorated so much that the so-called highest intelligent class of men cannot understand this Bhagavad-gītā. And he is posted as the professor in the Oxford University". (Lecture on BG 1.41-42 -- London, July 29, 1973)

Srila Prabhupada - "This Mahābhārata was compiled by Vyāsadeva for this purpose because strī, women; śūdra, the fourth class of the society, laborer class, worker class; strī, śūdra; and dvija-bandhu, and persons who are born in the families of brāhmaṇa, kṣatriya, but they do not act, they are called dvija-bandhu. 

For them, this Mahābhārata was compiled. It is called "Fifth Vedas." 

Four Vedas: Sāma, Yajur, Atharva..., Sāma, Yajur, Ṛk, Atharva. So this Vedic language cannot be understood by the less intelligent class of men who are known as woman, śūdra, and dvija-bandhu, strī-śūdra-dvija-bandhūnām (SB 1.4.25)". (Lecture on SB 1.2.13 -- Vrndavana, October 24, 1972)

Srila Prabhupada - "Dvija-bandhu means born in a brāhmaṇa family, but not qualified as brāhmaṇa. They are called not brāhmaṇa. 

They are called dvija-bandhu.

So this Mahābhārata was made by Vyāsadeva for these strī śūdra divja bandhūnām. 

Therefore Mahābhārata is called "Fifth Vedas." There are four Vedas, Sāma, Yajuḥ, Ṛk, Atharva, and Mahābhārata is the fifth Veda. 

And the essence of Vedic knowledge is given within the Mahābhārata, this Bhagavad-gītā. 

So although woman is inferior than the man, still, the Vedic civilization is so perfect that the man, as father, as husband, or as son, takes care, full care of the woman. 

This is Vedic civilization. Therefore it is said that mātuḥ priya-cikīrṣayā. The son was ready always to see that "Mother is not unhappy. 

My father has gone away. So she may not feel the absence of my father." This very word is very significant, mātuḥ priya-cikīrṣayā. He was always ready to take care of the mother. And the best care is to give her knowledge". (Lecture on SB 3.25.5-6 -- Bombay, November 5, 1974)

Srila Prabhupada - "Here is Vedic literature, Śrīmad Bhāgavatam or Bhagavad-gītā. They are all Vedic literature. 

The Mahābhārata is Pañcama-veda. The four Vedas are there, Sāma, Yajur, Ṛg, Atharva. And Mahābhārata is Pañcama-veda, the fifth Veda.

 Stri-śūdra-dvija-bandhūnāṁ trayī na śruti-gocarā (SB 1.4.25). Woman and śūdra and dvija-bandhu, they cannot understand Vedic language. It is difficult. 

For them Vyāsadeva made Mahābhārata. In the manner of studying history, Mahābhārata... Mahābhārata means the great history of greater India. 

So in that history, Vedic literature, Pañcama-veda, there is the Bhagavad-gītā, essence. 

So if you read Bhagavad-gītā, even if you read Mahābhārata, that is all Vedic literature, Mahābhārata, Rāmāyaṇa, the Purāṇas, the Upaniṣad, Vedānta-sūtra, and the Vedas, original Vedas. 

Original Veda is Atharva Veda. Atharva Veda was divided into four parts, Sāma, Yajur, Ṛg, Atharva. So they are all Vedic literatures". (Lecture on SB 7.12.3 -- Bombay, April 14, 1976)

Srila Prabhupada - "In this way the whole Vedic knowledge developed into four Vedas, 108 Upanisads, 18 Puranas, then summarized in Vedanta Sutra, and then again to benefit the less intelligent class of men like women, workers, and the degraded descendants of the higher class he made another fifth Veda known as Mahabharata or the great history of India.

The original Bharata and modern India are not the same. The original Bharata means the whole earthly planet. 

Gradually being sectioned, the modern India is only a fractional part of the original Bharata. 

So the knowledge is distributed in so many departmental Vedic knowledge, but the whole process is aiming at God-realization". (Letter to devotee -- Los Angeles 12 April, 1970)

Srila Prabhupada - "I am in due receipt of your letter dated September 28, 1974 and have noted the contents. 

Yes, the Mahabharata is an authoritative book. It is considered the fifth veda. 

But, quotations must be given from the original Mahabharata.

Regarding your question on demigod worship, there are so many demigods, and the qualities may be overlapping. 

Demigod worship is meant for materialistic men whether in goodness, passion, or ignorance. 

Those in the transcendental position above the qualities of the material world worship Visnu. 

Most people do not know that Visnu is the ultimate aim of worship. The varna-asrama system is organized with this purpose, to worship Visnu. 

So far we are concerned, we never recommend to worship any demigod either in goodness, passion or ignorance". (Letter to Ksirodakasayi -- Mayapur 18 October, 1974)