Pancha-Brahmans are the five fold manifestation of Lord Shiva and are named as Sadyojata, Tatpurusha, Aghora, Vamadeva and Ishana. Each five manifestations further manifest as five deities which are as Brahma from Sadyojata, Vishnu from Vamadeva, Rudra from Aghora, Maheswara from Tatpurusha and SadaShiva from Ishana.
Thus the primary Pancha Brahmas are:
➡➡Sadyojata, Vamadeva, Aghora, Tatpurusha, Ishana.
The secondary Pancha Brahmas which manifest from above primary Pancha Brahmas are:
➡➡ Brahma, Vishnu, Rudra, Maheswara, SadaShiva.
In the Vyavaiya Samhita Chapter 3 of Shiva Purana, Upamanyu states to Lord Krishna as:
श्रृणु कृष्ण महेशस्य शिवस्य परमात्मन ।
मूर्त्याभिस्ततं कृत्स्न्नं जगदेतच्चराचरम् ।।
स शिवः सर्वमेवेदं स्वकीयभिश्च मूर्तिभिः ।
अधितिष्ठत्यमेयात्मा ह्योतत्सर्वमनुस्मृतम् ।।
ब्रह्मा विष्णुस्तथा रुद्रो महेशानः सदाशिव ।
मूर्त्तस्तस्य विज्ञेया याभिर्विश्वमिदं ततम् ।।
अथाऽन्याश्चापि तनवः पञ्च ब्रह्मसमाहृया ।
तनूभिस्ताभिरव्याप्तमिह किञ्चिन्न विद्यते ।।
ईशानः पुरुषोऽघोरो वामः सद्यस्तथैव च ।
ब्राहाण्येतानि देवस्य मूर्तय पञ्च विश्रुता ।।
Upamanyu said, “0 Sri Krishna, Lord Shiva who is Paramatman pervades in the entire universe comprising of mobiles and immobiles in the form of Murtis. Shiva presides over all these by means of his own Murtis. His Atman is incomprehensible as said by the sages. His forms comprise of Brahma, Visnu, Rudra, Mahesa and SadaShiva which pervade in the universe. There are other images of Siva known as Pancabrahman, which also pervade the universe. There is nothing in the world in which he is not found present. The well known images of Shiva comprise of Ishana, (Tat)Purusa, Aghora, Vamadeva and Sadyojata.
Significance of Pancha Brahmans:
i) Significance in Cosmic Level:
In the Linga Purana Uttara Bhaga chapter 14 Nandi tells the significance of Pancha Brahmans to SanatKumara as:
सर्वलोकैकसंहर्ता सर्वलोकैकरक्षिता ।
सर्वलोकैकनिर्माता पञ्चब्रह्मात्मकः शिव ।।
सर्वेषामेव लोकानां यदुपादानकारणम् ।
निमित्तकारणं चाहुस्स शिवः पञ्चधा स्मृतः ।।
मूर्तयः पञ्च विख्याताः पञ्च ब्रह्माह्वाः पराः ।
सर्वलोकशरण्यस्य शिवस्य परमात्मनः ।।
क्षेत्रज्ञः प्रथमा मूर्तिः शिवस्य परमेष्ठिनः ।
भोक्ता प्रकृतिवर्गस्य भोग्यस्येशानसंज्ञित ।।
स्थाणोस्तत्पुरुषाख्या च द्वितीया मूर्तिरुच्यते ।
प्रकृतिः सा हि विज्ञेया परमात्मगुह्यात्मिका ।।
अघोराख्या तृतीया च शंभोमूर्तिरीयसी ।
बुद्धेः सा मूर्तिरित्युक्ता धर्माद्यष्टांगसंयुता ।।
चतुर्थी वामदेवाख्या मूर्तिः शंभोर्गरीयसी ।
अहंकारात्मकत्वेन व्याप्य सर्वं व्यवस्थिता ।।
सद्योजातह्वया शंभोः पञ्चमी मूर्तिरुच्यते ।
मनस्तत्त्वात्मकत्वेन व्याप्य सर्वं व्यवस्थिता ।।
In the form of Pancha Brahman, Shiva is the creator of the Universe besides being it's destroyer and protector. The learned people say that Shiva is both material and intellectual cause of the world. The learned people say that Shiva is the material as well as the factual cause of the three worlds, who has five forms. The great forms of Shiva — the supreme soul, who is worthy of the refuge of all the worlds, are five in number and are known as Pancha Brahmanas. lshana happens to be the first form of Shiva Paramesthi also known as Ksehtrajna. In this form, he is the knower of the field and enjoyer of Prakrti which is fit to be enjoyed. The second physical form of the lord is known as Tatpurusha, which again is equal to Prakriti as the abode of the supreme soul. The third physical form of the lord is known as Aghora, which form pertains to the cosmic intellect. It has eight related parts starting with Dharma. Vamadeva is the fourth physical form of lord Siva which pervades in all the living beings in the form of ego. What is called Sadyojata is the fifth physical form of the lord and is stationed in all the embodied beings in the form of mind.
Thus the PanchaBrahmanas presides over as:
Ishana➡ Kshetrajna and enjoyer of Prakirti
Tatpurusha➡Gunas of Prakirti
Aghora➡ Cosmic Intellect (Buddhi)
Sadyojata ➡ Mind (Mana)
ii) Significance in Bodily and Elementary Level:
In the Vyayaviya Samhita Shiva Purana chapter 3, Upamanyu states to Lord Krishna as:
श्रोत्रस्य वाचः शब्दस्य विभोर्व्योम्नस्तथैव च ।
ईश्वरीमीश्वरस्येमामीशाख्यां हि विदुर्बुधा ।।
त्वक्पाणिस्पर्शवियूनामीश्वरीं मूर्तिमैश्वरीम् ।
पुरुषाख्यं विदुः सर्वे पुराणार्थ विशारदाः ।।
चक्षुषश्चरणस्यापि रुपस्याग्नेस्तथैव च ।
अघोराख्यमधिष्ठात्री मूर्तिमाहुर्मनीषिणा ।।
रसनायश्च पायोश्च रसस्यापां तथैव च ।
ईश्वरी वामदेवाख्यां मूर्तिं तन्निरतां विदुः ।।
घ्राणस्य चैवपस्थस्य गन्धस्य च भुवस्तथा ।
सद्योजातह्वयां मूर्तिमीश्वरीं सम्प्रचक्षते ।।
The people of wisdom, consider Ishana as the presiding deity of the ear, speech, sound and all pervasive ethers. The persons Well versed in the Puranas find Tatpurusa as the presiding deity of the skin hands, touch and Vayu. The wise people know that Aghora is the presiding deity of the eyes, legs, colour and the fire. The devotees should understand that Vamadeva happens to be the presiding deity of tongue, anus, taste and waters. According to their Sadyojata is the presiding deity of nose, sex organs, smell and the earth.
Thus the PanchaBrahmans preside over elementary and bodily level as:
Ishana➡ Ether, Sound, Ear, Mouth
Tatpurusha➡ Air, Touch, Skin, Hands
Aghora➡ Fire, Colour, Eyes, Legs
Vamadeva➡ Water, Taste, Tongue, Anus
Sadyojata➡ Earth, Smell, Nose, Sex Organs.
iii) Significance in Panchakshara Mantra:
The Pancha Brahman Upanishad states as:
इत्येतद्ब्रह्म जानीयाद्यः स मुक्तो न संशयः ।
पञ्चाक्षरमयं शम्भुं परब्रह्मस्वरूपिणम् ॥ २४॥
नकारादियकारान्तं ज्ञात्वा पञ्चाक्षरं जपेत् ।
सर्वं पञ्चात्मकं विद्यात्पञ्चब्रह्मात्मतत्त्वतः ॥ २५॥
पञ्चब्रह्मात्मिकीं विद्यां योऽधीते भक्तिभावितः ।
स पञ्चात्मकतामेत्य भासते पञ्चधा स्वयम् ॥ २६
There is no doubt that the one who
understands this Brahman becomes freed (emancipated). One should chant the Panchakshara Mantra which is from Na to Ya (Namasivaya) and which is of the shape of five letters and is Lord Shiva’s body. After understanding the philosophy of the soul of Pancha Brahma, One should understand that every form is the form of those five. One who studies this knowledge of the soul of the Pancha Brahma would shine himself as Pancha Brahma.
Thus the Panchakshara Mantra represent Pancha Brahman as:
Sadyojata➡ Na kaara
Vamadeva➡ Ma kaara
Aghora➡ Shi kaara
Tatpurush➡ Va kaara
Ishana➡ Ya kaara
The Pancha Brahman mantra are itself from Vedas. Vedas recognizes various fold manifestation of Lord Shiva. For eg. In this chapter of Yajurveda Shatapatha Brahmana Eight Fold manifestation of Lord Shiva are described also known as AshtaMurti. In this form Lord Shiva after being born through Brahma enters Eight places: Fire, Water, Plant, Air, Lightening, Raingod, Moon Sun as Rudra, Sarva, Pashupati, Ugra, Asani, Bhava, Mahadeva, Ishana.
Similarly in the Brihadaranyaka Upanishad (which is itself part of Shatapatha Brahmana) 11 fold manifestation of Lord Shiva which are known as Ekadash Rudra are described as:
कतमे रुद्रा इतिः दशेमे पुरुषे प्राणाः आत्मैकादशः ते यदास्माच्छरीरान्मर्त्यादुत्क्रामन्त्यथ रोदयन्ति, तद्यद्रोदयन्ति तस्माद्रुद्रा इति ।।
‘Which are the Rudras ?’ ‘The ten pranas in the human body, with the Atman as the eleventh. When they depart from this mortal body, they make one’s relatives weep. Because they then make them weep, therefore they are called Rudras.’
Similarly the Five fold Manifestation of Lord Shiva or Pancha Brahman are also saluted in the YajurVeda Taittariya Arnayaka. And the five mantras present there describing Pancha Brahman are popularly known as Pancha Brahman Mantras. The Pancha Brahman Mantras are as:
सद्योजातं प्रपद्यामि सद्योजाताय वै नमो नमः ।
भवे भवे नातिभवे भवस्व माम् । भवोद्भवाय नमः ॥ (YajurVeda Taittariya Aranyaka 10.17.1)
I take refuge in Sadyojata. Verily I salute Sadyojata again and again. O Sadyojata, do not consign me to repeated birth; lead me
beyond birth, into the state of bliss and liberation. I bow down to Him who is the source of transmigratory existence.
वामदेवाय नमो ज्येष्ठाय नमः श्रेष्ठाय नमो रुद्राय
नमः कालाय नमः कलविकरणाय नमो बलविकरणाय नमो बलाय नमो बलप्रमथाय नमः सर्वभूतदमनाय नमो
मनोन्मनाय नमः ॥ (Taittariya Aranyaka 10.18.1)
Salutation to Vamadeva [the beautiful and shining One or the generous God]. Salutation to Jyestha [the Eldest, existing before creation]. Salutation to Srestha [the most worthy and excellent]. Salutation to Rudra [He who causes creatures to weep at the time of dissolution]. Salutation to Kala [He who is the Power of time responsible for the evolution of Nature]. Salutation to Kalavikarana [He who causes changes in the evolution of the universe beginning with Prakriti]. Salutation to Balavikarana [He who is the producer of varieties and degrees of strength]. Salutation to Bala [He who is the source of all strength]. Salutation to Balapramathana [He who suppresses all power at the time of retraction]. Salutation to Sarvabhutadamana [the Ruler of all the created beings]. Salutation to Manonmana [He who is the kindler of the light of the soul].
अघोरेभ्योऽथ घोरेभ्यो घोरघोरतरेभ्यः । सर्वतः शर्व
सर्वेभ्यो नमस्ते अस्तु रुद्ररूपेभ्यः ॥ (Taittariya Aranyaka 10.19.1)
Aghora form which is both Ghora (terrific) and aghora (non terrific). Salutation to Sarva (destructive) form of Rudra which is all.
तत्पुरुषाय विद्महे महादेवाय धीमहि । तन्नो रुद्रः
प्रचोदयात् ॥ (Taittariya Aranyaka 10.20.1)
May we know or realize the TatPurusha. For that, may we meditate upon Mahadeva and to that meditation may Rudra impel us.
ईशानः सर्वविद्यानामीश्वरः सर्वभूतानां
ब्रह्माधिपतिर्ब्रह्मणोऽधिपतिर्ब्रह्मा शिवो मे अस्तु सदाशिवोम् ।। (Taittariya Aranyaka 10.21.1)
May the Ishana who is the ruler of all knowledge, controller of all created beings, the preserver of the Vedas and the one overlord of Hiranyagarbha, be benign to me. I am the Sadasiva described thus and denoted by Pranava.
Regarding the name "PanchaBrahmanSanasthita" occuring in Lalita Sahasranaama, it denotes the form of Sri Lalita Devi where she sits over the PanchaBrahmans. Here sitting over PanchaBrahmans does not mean sitting over Sadyojata, Vamadeva, Tatpurusha, Aghora and Ishana. But it means sitting over Brahma, Vishnu, Rudra, Maheswara and Ishana which are also PanchaBrahmans (but they are manifestation of PanchaBrahmanas like Sadyojata... Ishana)
So, "PanchaBrahmanSanasathita" in Lalita Sahasranaama means who seats in the Aasana made up of Brahma, Vishnu, Rudra, Maheswara and SadaShiva.
As I discuss in my answer here Devi speaks in Devi Gita of Tripura Rahasya as:
My concrete form is the eternal couple — the Supreme Lord and Energy — always in undivided union and abiding as the eternal consciousness pervading the three phenomenal states of waking, dream and sleep, and reclining on the cot, whose four legs are Brahma (the Creator), Vishnu (the Protector), Shiva (the Destroyer) and Ishwara (Disappearance) and whose surface is Sadasiva (grace), which is contained in the mansion known as the ‘fulfilment of purpose’, enclosed by the garden of ‘kadamba’ trees, in the jewel island situated in the wide ocean of nectar surrounding the cosmos and extending beyond.