Hebrews 5 & 7

To the Hebrews, who were very familiar with the traditions in the old testament, Paul writes -

"So also Christ glorified not himself to be made an high priest..." (New Testament Hebrews 5:5)

But nonetheless, He was -

"...a priest for ever after the order of Melchisedec..." (New Testament Hebrews 5:6)

"Called of God an high priest after the order of Melchisedec." (New Testament Hebrews 5:10)

Alma taught the people of Ammonihah -

"I would that ye should remember that the Lord God ordained priests, after his holy order, which was after the order of his Son, to teach these things unto the people.
2 And those priests were ordained after the order of his Son, in a manner that thereby the people might know in what manner to look forward to his Son for redemption." (Book of Mormon Alma 13:1 - 2)

Paul also suggests there is a lesser priesthood than that after the order of Melchizedek as he questions the Hebrews -

"If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
12 For the priesthood being changed, there is made of necessity a change also of the law." (New Testament Hebrews 7:11 - 12)

It was the Aaronic Priesthood that administered the law of sacrifice as given in the mosaic law. The ordinances of this priesthood does not bring all the blessings of salvation -

"For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God." (New Testament Hebrews 7:19)

For this priesthood and -

"...law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster.
26 For ye are all the children of God by faith in Christ Jesus." (New Testament Galatians 3:24 - 26)

This is the purpose of the Melchizedek priesthood, -

"The power and authority of the higher, or Melchizedek Priesthood, is to hold the keys of all the spiritual blessings of the church—" (Doctrine and Covenants Section 107:18)

"And no man taketh this honour unto himself, but he that is called of God, as was Aaron." (New Testament Hebrews 5:4)

Ordinations of the Aaronic Priesthood -

"....were made without an oath..." (New Testament Hebrews 7:21)

But the greater priesthood is made

"...with an oath by him that said unto him..." (New Testament Hebrews 7:21)

And this oath -

"...is according to the oath and covenant which belongeth to the priesthood." (Doctrine and Covenants Section 84:39)

which is -

"...whoso is faithful unto the obtaining these two priesthoods of which I have spoken, and the magnifying their calling, are sanctified by the Spirit unto the renewing of their bodies.
34 They become the sons of Moses and of Aaron and the seed of Abraham, and the church and kingdom, and the elect of God.
35 And also all they who receive this priesthood receive me, saith the Lord;
36 For he that receiveth my servants receiveth me;
37 And he that receiveth me receiveth my Father;
38 And he that receiveth my Father receiveth my Father's kingdom; therefore all that my Father hath shall be given unto him....Therefore, all those who receive the priesthood, receive this oath and covenant of my Father, which he cannot break, neither can it be moved." (Doctrine and Covenants Section 84:33 - 40)