Is it a drop in the bucket for the GM, though?

I can't think of any sort of game where that would be a good idea. Not even Narrativist type games where you build the world in-play around PC concerns; 5 pages closes down far too many questions. Not traditional sandboxing where it closes off motivations, definitely not adventure paths where the GM has to fit 5 pages into a pre-written plot.
I guess it's least harmful for sandbox games with self-motivated PCs; the GM may not have to worry about it much and the player can use it in play as appropriate, perhaps. That sounds like what you guys are doing. Even in sandbox I've seen some really horrible, destructive backstories, though.
Like I said I don't expect him to. 5 pages isn't for him, its for me, because he asked he gets to see the same stuff I'm using to better RP my character. How much plot 5pages actually involves depends on the writing, I personally tend to write backstories more along the lines of "a day in the life" of my character. So its not five pages of me becoming a champion wrestler because I was raised by wolves and I how I defeated so-in-son in single combat. It's more about one specific event that defines my character and demonstrates how they react to certain stimuli.
But like I said, backstories are more for me than him. If he feels its too much to read I really don't care if he asks for a synopsis, but I don't write my backstories that way, too boring.
EDIT: I also make an effort to avoid "damaged" characters. Sure I pull the "orphan" trope from time to time, but only if birth is relevant to the backstory. Characters with severe emotional issues are not something I write well, and being the son of a therapist I know that mental health is an incredibly complex issue.
DOUBLEPLUSEDIT: Your comment reminded me of one of the long running complaints about "weird races" wherein the DM wonders whatever shall they do when the PHB includes something weird they don't like, and Timmy wants to play it. In regards to background stories, as much as playable classes and races, the DM IMO,
always retains the right to say "NO." and should be okay with having to exercise that right. If Timmy makes a background that he was raised in some place that doesn't exist, by some people the DM isn't interested in including and did some stuff the DM doesn't want referenced, beyond the ability to simply decline to include any reference to Timmy's backstory, the DM should also be OK with telling Timmy that his backstory doesn't fit the game.
HOWEVER: this is an issue I see pop up from time to time, why do you have players wanting to do things you don't want done in a game? Either:
A: you didn't clarify these things and it's really your fault.
B: You did and your players are disrespectful jerks.
If you failed to clarify what you're okay with in a game, you need to either own up and clarify ASAP, or suck it up.
If your players are disrespectful jerks who won't at least try to work within the bounds of your story, you need to tell them to shape up or ship out.