The 5th dimension, in a mathy geometrical sense, has been described as a "cursed" dimension. This is because of its symmetry groups, which are kind of sad compared to the stuff around it. A brief review of the first 8 dimensions:

• 1D is, as always, boring. It has bilateral symmetry only.
• 2D has an infinite number of rotational symmetries, all of which can be either flippable or chiral.
• 3D has a few symmetries based on the 2D ones, plus tetrahedral, octahedral, pyritic, and the beautiful H3 icosahedral symmetry.
• 4D is usually considered the best, as it has prisms of all the 3D symmetries, which I believe can be chiral independent of its base. It also has duoprismatic symmetries, basically a symmetry for every pair of numbers. It also has pentachoral, hexadecachoral, pyritic, demicubic, and hexacosichoral symmetries of its own. In addition to all of that, a 3D symmetry and a 2D symmetry can be combined together into a swirl symmetry, which I don't know much about.
• 5D, the "cursed" or "ugly" dimension, has the usual simplex (A5), hypercubic (B5), and demicubic (D5) symmetries that every above dimension has, plus products of lower dimensions. Most can also be chiral. This may not seem bad at first glance, but the problem with it is that all three of the symmetries are tiny and kind of boring, and prisms/multiprisms of lower-dimensional symmetries, while they can be arbitrarily complex, are not particularly aesthetic.
• 6D through 8D are not too much better than 5D, but they have the Gosset E6, E7, and E8 symmetries which are much nicer and rounder. 8D also has swirl symmetries that are combinations of a 5D and 4D symmetry.
• All higher dimensions are just as bad as 5D, except that 16D may or may not have swirl symmetries that are a combination of a 9D and 8D symmetry (we haven't managed to construct this, but relations to analogues of the Hopf fibration make it a possibility). Even dimensions also have a different type of analogue to the Hopf fibration for something called polytwisters that are related to swirl symmetry. I'm not sure if this other type makes actual symmetry types but if they do it means that every even dimension is better than 5D and odd dimensions above 8D. Dimensions that are multiples of 4 have a similar analogue but with the 8D one, though we don't think something like that would apply to the 16D ones.

So anyway, 5D is considered "cursed" and "ugly" because it doesn't have as many symmetries as the dimensions surrounding it (4D and 6D). In this article I want to try to convince you that 1. 5D is in fact the best dimension and not 4D, and 2. Symmetry does not define a dimension's aestheticness. I'll mainly be exploring this from the perspective of a 5D human analogue trying to appreciate geometrical beauty (if you explore it from a more mathematical standpoint, then 5D definitely is an ugly dimension).

1. 4D has codimension 1

This is another way of saying "4D objects are flat and lie in a plane in 5D", but it allows far more than having 4D objects on your wall. First of all, 4D designs can be painted, etched, engraved, etc. onto any flat surface. Think about our 3D world. As much as the icosahedron is cool, you can never truly appreciate it in its full glory because you can't see it all at once. Most graphic design involves polygons since they're simpler to work with on screens and signs, and when they do include polyhedra, they're always projections. 5D allows you to appreciate all the wonders of 4D in their true form, which is something 4D can never hope to offer. It also means you'll be able to include swirlchora, the 24-cell, duoprisms, etc. etc. in your graphic designs without needing any sort of projection at all.

Also, objects being flat grants you a lot more than being able to paint and engrave on stuff. Flowers now take full advantage of 4D symmetry in their petals, allowing you not only the godly appreciation of H4, but the ability to view it in the the beautiful format of a rose as you look at its pentagonal glory.

You can also have tilings of 4D space on your bathroom floors and wall, and since 5D Wythoffian operations apply to three different regular tilings of 4D space, plus their duals, all creating aesthetic arrangements, your possibilities are varied.

2. 3D has codimension 2

In 4D, neat things happen because of 2D being codimension 2. Because you can have a full polygon without going up or down, forward or backward, you can create Hindu deities and four/six-armed demons without the inconvenience of stacking them within each other's armpits. The same applies to legs, wings, eyes, and numerous other things.

While this isn't quite as impactful as 4D being codimension 1, 3D being codimension 2 allows some pretty interesting things, such as icosahedral leg arrangements being equivalent to bipedal, or allowing the phalanges/fingers in a bat or dragon wing to be arranged into tilings of 3D space. Given that 3D also has 8 Thurston geometries for non-Euclidean tilings to exist in, some of the possible tilings can get very interesting.

3. Symmetry is not the only measure of beauty

This applies to all dimensions, but perfect mathematical symmetry is only one way things can be beautiful. Color, arrangement, juxtaposition, etc. exist in every dimension, and are often far more important. There's also beauty in chaos and randomness as well. And fractals, commonly thought of as one of the most beautiful things to come out of math, exist in every dimension. The famous Mandelbrot set is only bilaterally symmetric, not even rotationally symmetric at all, and yet it's full of structures considered to be beautiful. Which brings me to:

4. Having symmetry vs. not having it matters MUCH more than which symmetry you have

As I said, the Mandelbrot set is bilaterally symmetric. So is nearly every animal found in nature on Earth. For almost any animal, there is someone who thinks they look cool, and while they would probably take issue if bilateral symmetry was removed, they also don't mind that they aren't icosahedral or eight-fold rotational symmetry or something. There's also something cool related to this that I've thought about.

A lot of 4D creature designs give them rotational symmetry with codimension 2 instead of bilateral symmetry (or maybe it's just me, idk). But biologically this is likely wrong in my opinion. Cells prefer to divide into two, and high-order symmetry isn't really an advantage for evolution to consider. I speculate that realistically, higher-dimensional animals/creatures/humans would remain only bilaterally symmetric and have a second axis of asymmetric that acts something like front-to-back, but with a different slice series than it. This applies to 5D as well.

So, it's 5D mythical creature time! Pick any number of bilaterally symmetric 3D creatures, even if human or mythical, and place them as points on a 2D plane anywhere you want. Now look at what you've constructed. No matter what creatures you chose and where you put them, there is some good way to connect them with other 3D slices to make a complete, bilaterally symmetric 5D creature. It's up to you to find what those slices are, and there will be multiple correct ways, but the freedom is astounding. Screw centaurs, you can arrange a human, a horse, a centaur, and a mermaid at the corners of a square and connect them to form a new creature that can't exist in any lower dimension. This applies to 4D too, but you can only arrange them in a line, which prevents you from forming polygons or doing anything except stacking them horizontally.

Moving on from that little tangent. Bilateral symmetry, while already good, is of course not the limit. You have 2D, 3D, and 4D symmetries as well, which are all good, and products of lower dimensional symmetries (such as 3Dx2D) aren't exactly bad, just that you need some extra design to make them look nice.

5. Roundness doesn't have anything to do with symmetry