Just wanna pick your gray matter. I'm thinking up a setting that's kinda like a pocket dimension wherein there are no gods. A few powerful beings, maybe, but nowhere near the level of gods. So I'm wondering how I can explain divine magic.

Got any ideas?

And if this is addressed in the rulebooks somewhere, please tell me where.

Thanks.

Gods are generally associated with portfolios: Life, Death, War, Creation, Trickery, etc.

In some interpretations, Gods are the sources of those things, and the magic associated with them, but in other interpretations, Gods act more like stewards. The magic and natural forces already exist within the world, and Godhood is essentially the ultimate way of tapping into those resources. If all of the Gods were dead, or a particular portfolio were rejected by living gods, then that resource would be left without a figurehead, but not gone from the world. Those who worship that abandoned "concept" might find themselves tapping into the raw energies directly.

In essence, "magic" and "nature" has a will of its own, in the same way that bacteria spreads or gravity pulls matter together. If someone creates the appropriate conditions, those forces automatically respond in kind. "Life Magic" might naturally be drawn toward a "Life Cleric", because they resonate at the same "frequency". No one is pulling the strings, it's just the raw fabric of the universe doing what it has always done.

"Godhood" is then effectively a Magical Black Hole, where an individual draws in so much magic that they become self-sustaining.

First question: do you even want or need divine magic? Second question: if that's a yes to the first, why?

I've seen it explained before that faith is the actual source of power, rather than the god itself. Your belief and conviction empower you to perform miracles. This is pretty easy to do in 5e where you really just choose a domain, and the god empowering that domain for you is kind of secondary (and paladin oaths are even farther conceptually removed from the gods). Contrast this to the previous edition where your choice was which god you worshipped and that choice limited the domains you could access.

According to the DMG

As far as the game’s rules are concerned, it doesn’t matter if your world has hundreds of deities or a church devoted to a single god. In rules terms, clerics choose domains, not deities, so your world can associate domains with deities in any way you choose.

so you can explain Domains however you like without a god. 

also from DMG

In the Dark Sun setting, the gods are extremely distant — perhaps nonexistent — and clerics rely instead on elemental power for their magic.

I have actually done this exact thing! (Don't tell my players, they don't know yet)

The way I have done it is by developing religions within the space. If there is a weird purple clot in the otherwise black sky? It is the icon of the warship. If there is a single river that everyone drinks from? There is a religion about that.

Gods get their power because of the people that believe in them. After all a god without followers is nothing but a husk. There is no reason why a bunch of people worshiping something that is not an individual can not empower each other via their belief. If enough people put their belief into the all mighty purple spot in the sky, and I decide to become a priest of the purple spot and people start believing in me it would make sense that I would gain power because of my shared faith with people. PRIASE BE THE PURPLE SPOT!