The writer of Hebrews picked up pen (or quill) with the purpose of warning his Jewish Christian readers not to return to life and faith under the Old Covenant. That covenant was obsolete (8:13), and to return to it would be in essence to “depart from the living God” (3:12). In order to encourage them to continue believing in and following Jesus Christ, the Mediator of the New Covenant, the author demonstrated that the New Covenant is superior to the Old Covenant. At chapter four, verse 14 the writer of the epistle began to show the superiority of Christ, our “great” High Priest over the high priests who functioned under the Old Covenant.
In chapter 5, the author compares and contrasts Jesus with the priests of the Levitical order (5:1-11). What is true of both is that no man may take the honor of serving as high priest to himself, but must be called by God (5:4). God called Aaron and his sons to serve as priests. God the Father also called God His Son Jesus Christ to be a High Priest (5:5-6). Jesus was appointed a High Priest after the order of Melchizedek since He was not a descendant of Levi, a point the author makes later (7:12-14). One of the glaring contrasts between Jesus and Aaron is the length of ministry. Jesus is a priest forever, but Aaron and his descendants were prevented by death from continuing (7:23). Because Jesus continues forever He is able to save eternally those who come to God through Him (7:24-25; cp.5:6, 9). Another important contrast is the nature of the priests. The priest who served in the Levitical priesthood sinned, and was therefore required to offer sacrifices for his sins as well as for those of the people (5:2-3). Jesus is sinless and had no sins for which to offer sacrifices. He himself was the sinless, spotless Lamb of God sacrificed to take away the sins of the world! The sacrifices offered by Aaron and his sons were shadows of the “THE” sacrifice Christ offered. To return to the Old Covenant and its sacrifices which could never take away sins was to depart from the living God Who gave His only Son as the only sacrifice through which one could be completely and forever forgiven of sins.