The Order of Melchizedek

This Sunday's reading from Hebrews 5:5-10 hearkens back to Genesis,

 So also Christ did not glorify himself in becoming a high priest, but was appointed by the one who said to him,

‘You are my Son,

   today I have begotten you’;

as he says also in another place,

‘You are a priest for ever,

   according to the order of Melchizedek.’

In the days of his flesh, Jesus offered up prayers and supplications, with loud cries and tears, to the one who was able to save him from death, and he was heard because of his reverent submission. Although he was a Son, he learned obedience through what he suffered; and having been made perfect, he became the source of eternal salvation for all who obey him, having been designated by God a high priest according to the order of Melchizedek.

Who was Melchizedek? Go back to  Genesis 14:17-20, NIV,

After Abram returned from defeating Kedorlaomer and the kings allied with him, the king of Sodom came out to meet him in the Valley of Shaveh (that is, the King’s Valley).  Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High,  and he blessed Abram, saying, "Blessed be Abram by God Most High, Creator of heaven and earth. And praise be to God Most High, who delivered your enemies into your hand." Then Abram gave him a tenth of everything.

Melchizedek seems to be the first priest of God, and he was a king. His order is mentioned in Psalm 110:4,

The Lord has sworn and will not change his mind: "You are a priest forever, in the order of Melchizedek."

In researching how this applies to Jesus, I came across this comment in a discussion group, 

"...the name Melchizedek, like most Biblical names is also a regular word, in this case two words «Melech-Tzadik», meaning roughly «King-Priest». The significance of Jesus belonging to the order of king-priests, or holy-kings is that he, as the Messiah would ultimate replace both kingly and priestly orders existing at his times, by combining the two in himself."

Agreed.

I hope that clears things up.