Demonstrating its existence, beyond our 3D universe, is one of the most exciting and controversial areas of modern physics.
Physicists have been searching for it for a long time, and will continue to do so until they find it.
"What is the 5th dimension? I know that the 1st is height, the 2nd, width, the 3rd, depth, and the 4th, time, but nobody seems to know what is the 5th!".
That was the question that Lena Komaier-Peeters, a 12-year-old girl, sent to the BBC detectives, the geneticist Adam Rutherford and the mathematician Hannah Fry, who went to Geneva, Switzerland, to investigate.
In Geneva, they visited the place where what is probably the most amazing experiment with time and space, the CERN - the European Center for Nuclear Research - and they asked particle physics Rakhi Mahbubani to help us to understand.
"Imagine a channel that is narrow and long, with boats of different sizes navigating it.
"If you have a huge cruise ship that occupies almost the entire width, you can only move along the canal, you do not have the possibility to move wide, so from the perspective of that cruise, the channel only has one dimension.
"If what you have is a sailboat, you can zigzag wide." From the perspective of the sailboat, the canal has two dimensions.
"If you travel in a submarine, you would experience both length and width, but also depth, from that perspective, the same channel has three dimensions."
We are submarines: we live in 3D ... and physicists, however rare they may seem, too, then ...
--- Why do so many insist that there are other dimensions? ---
"A very convincing reason is that we really do not understand why the force of gravity is much weaker than the other fundamental forces we experience.
"If I give you a magnet that people put in refrigerators and any key, the magnet can lift the key very easily.
"The magnetic force of that little magnet surpasses the gravity force of the Earth, which is huge, which is pulling the key in the opposite direction."
True, but why does that imply that there are other dimensions?
"The hypothesis is that gravity, like the submarine in the channel, can experience additional dimensions, while we do not have that capacity, and it dissipates in those other dimensions and that is why we feel it is very weak."
Then, the force of gravity would be diluted.
--- A concept with a long 4th dimension ---
The concept of additional dimensions may seem futuristic, but the idea has existed for a surprisingly long time.
It became popular in the world of mathematics when the German Bernhardt Riemann demonstrated in 1854 that there could be more than 3 dimensions in geometry (although he had a nervous breakdown in the process).
Later in the same century, the British mathematician and science fiction fanatic, Charles Howard Hinton, designed a four-dimensional hypercube called "teseract".
A tesseract is a 4-dimensional analog of a cube, just as a cube is a three-dimensional analog of a square. The model is a theoretical projection of a four-dimensional cube over three-dimensional space.
Along with science came art, and the concept of extra dimensions appeared in works by Oscar Wilde, Marcel Proust and HG Wells (and the tesect plays a prominent role in Marvel comics). He also inspired Cubist artists such as Picasso, who tried to represent more dimensions in his paintings.
However, until now, nobody has been able to prove that they really exist.
That is exactly what they are trying to do at CERN, and to test theories, we need experiments.
--- How to discover the mysterious 5th dimension ---
First, you need a huge object to find the smallest fundamental particles in the Universe.
The one they have at CERN is called Large Hadron Collider or LHC (for its acronym in English: Large Hadron Collider), a proton-proton accelerator of 27 km in circumference.
With it, particle beams are shot at almost the speed of light so that when two protons collide they create all kinds of other particles.
If current theories are correct, there is a tiny chance that one of the subatomic particles in that collision is something called a graviton.
Quantum physics tells us that each force has a related particle that carries it. For example, light is transported by photons. So gravity should theoretically be transported by gravitons, only we have never observed them.
But they could be the key to unlocking hidden dimensions.
That is why CERN scientists have not stopped looking for 14 years.
And they do not lose hope.
Although, there are other theoretical physicists who are not as optimistic, as Sean Carroll, Caltech, in California.
"We are very sure that the gravitons exist, what we are not sure of is that they can be discovered with the Large Hadron Collider, in fact, the opposite: you have to be very, very, very lucky to be able to find gravitons in the GCH.
"There are theories and we are testing them but if the gravitons were there, we could have seen them easily and we have not seen them, so the probabilities are minimal.
"But, of course, it is very worthwhile to look for these other dimensions, because if we were to find them, everything we think about the fundamental laws of nature would change: it would be a transcendental discovery.
"If we do not see them, it does not mean they're not there, but our experiments are not good enough yet, if we keep trying, we'll hit the nail on the head someday."
And if we hit the nail on the head and reveal those much sought after dimensions, there are actually ...
--- How will they be? and where have they been hiding? ---
"They are everywhere," replies physicist Sean Carroll, but adds: "they do exist."
"You have to get into the mentality of physicists to understand what they mean when they say the word 'dimension'.
"We tend to believe that a dimension is a place to which you go and is possessed by strange creatures.
"A dimension is simply a direction in space, at this moment we know three, which we could call 'up-down', 'left-right' and 'forward-back'.
"Just as there is no point in saying 'where is the dimension' up-down '... it is everywhere! The same will be true of the other dimensions.
"What we know for sure is that they are hidden to us in some way, so they could be very, very, very small, so much so that we will never see them - that's the easiest way to hide.
"But there are two other possibilities: one is that they are half small-one millimeter or one tenth of a millimeter-and the other is that the dimensions are infinitely large but we can not reach them because we are trapped in a subspace of the Universe's lower dimension.
The branes would be membranes that maintain our Universe with its 4 dimensions in a space with multiple dimensions.
"That's something that physicists sometimes call the brane cosmology (a strange way of saying membranes like those that limit our 4-dimensional Universe within a space of superior dimensionality called 'bulk').
"If that is true, there could be multiple branes, multiple subspaces of bi, tri, tetra, and five-dimensional parallels, in that sense there could be parallel worlds incorporated in these other dimensions."
Something that does seem to be true after all this is that physicists have proved without a doubt the existence of a wonderful dimension: that of the imagination, the starting point of so many great discoveries.