Hebrews 7:3-5 - See how great this man was

7:3

“He is without father or mother ...” This could be taken literally, but that would probably be  a mistake. In the Old Testament we find that there is a great interest in genealogy. When someone is introduced in the Old Testament, we almost always (but not absolutely always) are given some details about their ancestry. We are also told about their death. With Melchizedek this is not the case, and this is probably what the writer is referring to. He was a type of Christ, prefiguring the eternal priesthood of Christ.

7:4,5

“See how great this man was ...”. The primary purpose of the writer is to demonstrate that Jesus is our great High Priest, infinitely superior to the Levitical priesthood. A symbol of the greatness of Melchizedek was that Abraham gave him a tithe. The Levites could also take a tithe, indeed there was a commandment for them to do so. But they took it from their brothers, from people who were just like them. In contrast, Melchizedek was set apart from Abraham.