The passage which begins at 5:11 and ends at 6:20 is a lengthy pastoral exhortation. It is an interlude. Before the author explains the doctrine of the high priesthood of Christ in the order of Melchizedek, he exhorts his readers to faithfulness. First, he admonishes them because of their dullness in learning the basic doctrines of God’s Word. Next, he delineates what these elementary teachings are: repentance, faith, baptism, ordination, resurrection, and judgment. He exhorts the recipients of his letter to advance in their understanding of these teachings.Throughout the epistle the author warns the Christians against the sin of unbelief (3:12; 4:1, 11; 10:26, 29; 12:15, 28-29). He describes the rebellious Israelites who perished in the desert because of this sin (3:16-19). In 6:4-6 the author pursues that same theme by referring to those persons who have hardened their hearts after receiving a knowledge of the truth. These people continue to crucify Jesus and to despise him. They do so in open rebellion. For such persons, says the author, there is no possibility of being brought back to repentance. They are lost forever.
This observation serves as a warning to the readers not to fall into the sin of unbelief, but to demonstrate their diligence in exhibiting the qualities of faith, hope, and love. The author singles out the virtue of hope and encourages them to make hope a priority in their spiritual lives. He commends them for their loving care shown to people in need and assures them that they are the recipients of the blessings of salvation. He exhorts them to cultivate hope. He points to Jesus, the forerunner who has entered heaven as high priest and who by his presence in heaven guarantees them entrance.
Hope is anchored in the finished work of Christ, who atoned for the sins of his people.