Is the flat curvature of the universe in the 5th dimension?

Several topics here:

No 5th dimension. Not even a 4th (spatial)

You're on the right track: The Universe being "flat" does not mean "like a table top", just like it being "spherical" and "hyperbolic" don't mean like a ball or a saddle. Those terms are just 2D analogies, whereas the Universe has three spatial dimensions. Like any analogy, they are great for understanding some things, but shouldn't be taken too far.

For instance, the sum of the angles of a triangle, the fate of parallel lines, and the volume of some region in space can be more easily visualized in 2D than in 3D. You can understand that a triangle going North Pole→Congo→Indonesia→North Pole has 270º rather than 180º. But whereas the 2D surface of Earth curves in 3D space, a 4th spatial dimension is not needed for our 3D Universe to curve (not to speak of a 5th). And imaging why a triangle consisting of what seems to be completely straight lines from Earth→GRB090423→EGSY8p7→Earth should not have 180º is difficult, but nonetheless perfectly possible.

The Universe is not a ball with you in the center

When you look around in the Universe, it looks like a spherical ball with you in the center, but that's only because what you see is everything from where light has had the time to reach you in 13.8 Gyr, i.e. since Big Bang. Everything inside that sphere is called the observable Universe, and it's bound by the so-called particle horizon. In the 2D analogy, you can say that Earth looks like a flat disk, but only because that's how far you can see. Again, don't take this analogy too seriously, since the reason here is just the curvature of Earth, and not that Earth has only existed for $10^{-4},mathrm{s}$.

Curvature

The dynamical and geometrical properties of the Universe depend on its expansion rate ($H_0$), the densities of its components (the "Omegas" of baryons, dark matter, dark energy, radiation, etc.), and its "intrinsic" curvature, which can also be written like a density parameter $Omega_k$. The latter is found to be $0.000pm0.005$ (Ade et al. 2015), but as you say, if it's less than $sim10^{-4}$, we may never know (Vardanyan et al. 2009).