Jesus used the terms "Son of God" and "Son of Man" inter-changeably in many places in scripture, to convey that he is both God and man. In the context of John 5:27, wouldn't it make more sense for Jesus to say that the "Son of God" has the authority to judge?
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin. Hebrews 4:15
Come Judgment Day, when He passes all His righteous judgments, there won't be a soul who won't be watching it all with amazement. "Shall not the Judge Of All The Earth Do Right?" - Genesis 18:25.
All the impossible situations, the what-ifs theologians manufacture by the thousands, will be taken care of, every person, every act, every detail, and every word (Matthew 12:36-37).
Hell will be capable of any punishment and heaven will be infinitely more capable of any reward than any of us can imagine.
But here's the Big Deal: instead of a far-out Judge in some mystical heavenly places, we've got a Judge who came to live here among us, faced every single temptation and trial and struggle any of us have ever faced, whipped them all hands down, and has the wounds and scars to prove it!
So can you imagine anyone proposing as an excuse, "You don't know what I was going through!"
Isn't He Brilliant, choosing to judge us as the Son of man, thereby obliterating our crummy excuses?