Panchakshari and Shadakshari mantra

Shiva is the great purifier as well as the Adiguru (primal guru). He is the deity (or archetypal energy) that purifies our wrong doings and helps us to burn up negative karmas. He is the source of knowledge and educates the heart and mind in the path one follows. He is the original guru as taught by Patanjali: Ishvara is Purusha, Aum is Ishvara, the teacher of the earliest Gurus.

Panchaksari Mantra

Panch means 5 and akshara means syllables, so the Shiva panchakshari mantra is the 5 syllable Namah Sivaya mantra. Namah Sivaya is 2 words and 5 syllables. It takes the energy of the 2 nd house (speech, traditional study, Masters degree, etc.) to the 5 th house (bhakti, mantra, yantra, tantra, intelligence). Shankaracharya was a great jnana yogi who advised the 5 syllable mantra, for its ability to open one to the knowledge of the Self which is Siva.In the Shiva Purana, it is Shiva that teaches the panchaksari mantra to Brahma in order to give Shakti to his forms. When the world is darkened by sins and evils it will be the panchaksari that will embark one on the mukti marga (path of liberation).
The 5 aksharas can be empowered each separately to give birth to the mantra for those who know mantra sadhanna. Aum NaM Namah Sivaya, Aum MaM Namah Sivaya, Aum SiM Namah Sivaya, Aum VaM Namah Sivaya, Aum YaM Namah Sivaya, (can each be done 108 times with Rishi, Chanda, Devata to give birth to the mantra).

	Na	Ma	Si	Va	Ya
Rishi	Gautama	Atri	Vishwamitra	Angirasa	Baradwaja
Chanda	Gyatri	Anustup	Tristup	Brihati	Virat
Devata	Indra	Rudra	Hari	Brahma	Skanda
Face	East	North	West	South	Upwards
Swara	Udatta	Udatta	Swaritta	Swaritta	Udatta

At the end of this chapter in the Shiva Purana (which has much more detail than given here), Shiva talks to Parvati. He tells Devi that Her mula mantra (root mantra) is also panchaksari, but it becomes Namah Shivayai. We then have a similar variation for Shakti Ma.

Shadakshari Mantra

Shad means 6 and akshara means syllables, so the Shiva shadakshari mantra is the 6 syllable Aum Namah Sivaya mantra. Aum Namah Sivaya is three words and 6 syllables- so it takes the 3rd house energy (parakrama) to the sixth house. Sixth house rules karma/works/service and also shad-ripus (our weaknesses). So Aum Namah Sivaya is best for karma yoga and purification of our bad karma and bad habits.
In the Shiva Purana, it is Krsna that teaches the shadakshari mantra. He says it colors peoples heart and makes them happy (loka chitta), it gives artha (wealth and moksa (spirituality) and is ornamented with a variety of siddhis (perfections). It is the essence of divinity (devasara), and the root of all vidya (nikil vidya). It is like and acorn of a banyan tree, giving rise to the greatest vidya (knowledge/science).
The five syllables are the five faces of Shiva, it is Shiva himself, it is naturally part of him as speech. The mantra is the devata, they reside together as speaker and spoken word. When Shiva himself Chants Aum, we have Aum Namah Sivaya.
It is said to be a medicine of all dosas (problems) of samsara. The name of Shiva is specific for removing putra doshas (problems related to having children). When there is no Sun we are enshrouded in darkness, the name of Siva is like the light of the Sun. It gives limitless omniscience (sarvajna), bliss (anandamaya sankara), and liberation (moksa). The Shadakshari is the knowledge of Shiva (Shivajnana), and it is the ultimate objective (paramapada).