It's not intractable, but it is a challenge. (Well, not "five"; I kinda hate that expression. But "scientifically interested layman" isn't beyond reach.)
Try it this way: Quantum mechanics rules are the "real" rules of the universe: objects don't have exact positions or locations. Rather, what you get is a wave that describes the object. One way to interpret that wave is that it predicts the probability that it could be at any particular place. The total behavior of the object is the sum of those probabilities. It really is in every single place, all at once, though "more" some places than others. These waves can even cancel out. That's very much at odds with what we expect.
Here's the thing with probabilities: the more of them you add up, the more they behave like the average. That is, there's a lot of uncertainty in the roll of a 20 sided die. But you know that if you roll it a thousand times, the average is going to be very close to 10.5.
Real-world objects contain far, far, far more than a thousand objects. If you work the sum of the quantum waves for that many objects, what pops out is remarkably like plain classical physics. So, everything you see looks like ordinary physics.
But if you design your experiment carefully, you can make some of the quantummy behavior show up. The most classic one is the two-slit experiment: you restrict the particle's path to one of two places, and you get interference waves. But if you modify the experiment so that it is interacting with large-scale objects like a detector somewhere in the process, the waves vanish. (A detector is something that has large-scale changes between the particle's presence and the particle's absence.) The confusing part is that you can put the detector in places where you wouldn't expect it to have an effect, but since the particle is "everywhere", it affects it in counterintuitive waves.
Proving that for certain turns out to be tricky. The difference between "the particle really is (partly) everywhere at once" and "the particle is actually in only one place, but you can't tell" is pretty subtle. You can show it by carefully counting up "entangled particles", where the two probability waves are linked. It would be natural to think that particles were exchanging information to maintain the linkage, faster than the speed of light, but the quantum rules actually rule that out. Proving it for certain is hard, since you're talking about very tiny things and very fast speeds. We actually have been doing it for decades, but since it's so hard, there were usually loopholes. This experiment finally nails the last of them shut.
The solution to the chicken-egg problem lies in the behavior of the sums: big objects behave like you expect them to because the probability of them not doing so becomes vanishingly small. There's still some fiddly bits: that "vanishingly small" isn't quite zero and nobody exactly knows where it goes. Some say "another universe"; others (like me) just put our fingers in our ears and say "I don't know but shut up and calculate la la la".