Time is not a dimension in the same way the other 3 are.
I had trouble imagining a 4th spatial dimension until recently, and then I saw the following example:
Imagine you are looking at a box (square) drawn on a piece of paper. That square and anything else drawn on the paper is in two dimensions. If you draw a ball inside of the square (a circle), it is completely enclosed and cannot be taken out of the square in those two dimensions without intersection with one of the sides of the square.
However, if you lift that 2D ball in the third dimension (the one you see as the observer in the experiment), you can make it "fly" above the square walls and put it on the other sides without intersecting the square sides. For you, the ball went above the square walls, but from the 2D point of view of the square and the ball, the ball seemingly phased through the walls because there is no such thing as height.
Now imagine the same thing with a box in 3D and an actual ball. If you put the ball in the box and close the lid, the ball cannot escape the box. However, in the fourth dimension (not time, the actual 4th spatial dimension), you could move the ball out of the box by pulling it in this new dimension and for us 3D observers it would seem like the ball phased through the box walls.
> ELI5: I understand 4th dimensional space.
How can you understand 4d, but not 5d? Here is my suspicion: If you mean "time" as fourth dimension there is a problem, as that is *not* 4 dimensional space. It is three dimensions and time, and "time" isn't actually a proper dimension, just the result of things happening in 3d-space.
Here is my take on "time", and what "time" and "space" actually mean. It also ties into entropy a lot, and sorry for the wall of text but I think we need to dive a bit deeper into this:
Let me start with the Big Thing, please stay with me: Time does not exist as actual dimension. Time is an illusion of "stuff happening in the physical world".
Imagine yourself to be in a room where no outer stimulus comes in. No light from a window, no sound from the other side of the door. Now, there is also nothing in the room itself that changes, no water tap with dripping drops, no breeze from a ventilator, no dust settling, no nothing. How could you tell that "time" passes?
You feel your own heartbeat, you feel your breathing. If you wait long enough you feel the need to eat, to drink, to sleep, to go to the toilet. If you wait long enough your nails and hair grow. But let us assume for some reason you do not have to, you just sit there and... sit there. How could you tell "time" passes?
You cannot - unless you move your hand. Unless you get up. Unless you take an object and let it drop so it falls down.
Now you suddenly can tell *something happend*. A moment ago you were sitting on the chair, now you stand. The physical space has changed and there are two states, one before you got up and one after. If you let something drop you create a whole lot of differing physical states in space: you have a thing in the hand, it drops, it drops further, it drops faster and faster and faster... and it hits the ground and rolls under the bed.
By observing what happens in the physical space you can tell a passage of what we now call "time". You can also tell that "the time it took you to move your hand was shorter than the time it took you to walk through the room", this means you somehow start to quantize a new observable beyond mere "where is an object in the space I am in" in the universe: time.
Our observation of time is very unprecise. Everyone knows that "time flies if you have fun" and stretches and strechtes if you are bored - on the other hand in our memory the day where we had lots of fun and did a lot of thing was much longer than the one we just waited out. To remedy this we build machines that repeat the same movement in space as precise as we can.
A pendulum swings. A water drop dripping down from a defined opening (i.e. a water clock). A spring is wound up and makes some axis turn which moves a digit. We then count the repetitions and say "Ok, 60 of those is a minute, and 60 of those is an hour" or similar. The most simple clock is the sun, we say "If it is right above and then again, we call it a *day*". If a season repeats because earth fully turned around the sun we call it a *year*.
So far so simple. We get the impression time exists because "stuff" happens around in the universe - and that includes our cells that grow and die and finally we grow and die as that is just chemical (fundamentally physical) proceedings in space.
Now for entropy:
In the most simple approach entropy is a measurement of "Order in the Universe". In very broad strokes: The higher the entropy the less ordered is the universe, meaning there are more states. A piece of wood has a lower entropy than the burned piece of wood. Now, in physical space things only happen *on their own* where the entropy is increased. So a ball falling down happens on its own because it increases the entropy. You have "ordered" energy in the form a ball lying on a table. If it falls down it loses that energy by disturbing all the air molecules it falls through, it hits the floor and makes all those molecules in it vibrate, the ordered energy from the ball on the table is now very, very unordered all over the room and this means: the entropy in the room has increased from state 1 (ball on table) to the new state (ball has fallen down).
We call this "Energy is scattered all over the place and thus entropy increases" as "time moves forward". Because, on their own, balls do not fall up back on the table, cells do not "undie", a set of fallen deck of cards does not order itself again. Because that would require the entropy in the room to decrease again and the room taking a "more ordered state" (meaning the cards are not lying all over the place but are nicely on a stack, possibly in a specific order, i.e. all colors together etc).
I wrote that entropy does not decrease on its own but you very much could go around and pick up the ball or the cards again, you might even order them again and put them back on the table. So you cheated entropy? You restored the highly ordered state of energy again? Yes, indeed, you did. But by that you increased the entropy in the room due to moving around, calling energy from your muscles and turning them into heat that now is in the room. You ordered the system of "ball and table", but the *total* entropy in the room (universe) went up - and as such you can tell that "time has passed forward between state 1 (deck of scards scattered) and state 2 (deck of cards neatly on the table)".
Now one thing missing from your question: Muller writes about "improbable". Imagine the room has a billion billion billion possible states where the ball is on the floor, the air molecules it shoved aside are scattered, the molecules in the floor have swung and all the ball's energy has dissipated as heat and increased the entropy. Of course (yes, of course!) there is the hypthetical case where all the molecules are just randomly happen to just move in the reversed direction, all the air goes back where it was, all energy, by pure chance, transfers back in the ball and it comes to lie back on the table. That totally can happen and in that case you would observe the ball... uhhh... falling (?) back onto the table.
In that case the entropy in the room (universe) would indeed have decreased on its own, you now had a - from an energetic point of view - more ordered state. Time would have moved "forward" but the entropy would have decreased. Yes, that is possible. It is just that the chance for that is 1 to a billion billion billion so we simply do not observe that in the macroscopic world. And that means "it does not happen" but if you are mathmatically correct, as a physics book should be, you say "it is highly improbable".
Now what with the actual "4 dimensional space". Imagine 1d to be a line. I can tell you where you are by giving you a coordinate, for example you stand at "56 meters from zero" or "-2 meters from zero". This position is called "x".
Now, 2d adds another line, in a right angle from the first. You can now stand on a plane and I can tell you where you are by giving two coordinates, one on one line and the other on the other. Let us call them "x" and "y". I could tell you are "56 meters on the x-line from zero and 3 meters from zero on the y line" and you would know where you are standing in that 2d-plane.
If you add a third line that needs to be in a right angle to BOTH of the other lines, you get a height. This is our 3d-space, and you know where you are if you know your position relative to zero and you can conveniantly tell that by knowing you are x, y and z along the lines. Maybe at 56 from x, 3 from y and like 10 meters above the ground. You know where you are in space and we can start to calculate positions of all kinds of physical objects, for example ones that fall, and derive the laws of physics from them, e.g. the law of gravity.
Now, what happens if you add a fourth (and fifth and... tenth) dimension? Well, in our 3ds-space, where do we add the next coordinate? When we simplified to 1d and 2d, we could easily do it. We just used less dimensions than we have. But where to put a 4th and 6th spacial line? We cannot, as we only think in 3d, our brains are only made for 3d, our lives only happen in 3d.
We very fundamentally cannot imagine 4d-space, but we can make an analogy: Imagine you are a person living in flatland, in the 2d-plane and suddenly someone comes along and tries to tell you about a "mystical third dimension that goes... *up*". What is this "up" he talks about? You have no way to tell what this "up" is and it gets even more confusing: imagine there is a ball that bounces on the plane of flatland. You could observe a dot that gets bigger and bigger as the ball contracts, and then smaller and vanishes when it goes up again. For us that is trivial to understand, but for a flatlander that is a big mystery. Not only does he not understand where the ball comes from (from higher dimension!) but he might not even know what a "ball" is and why it would do what it does.
To imagine a 4th spacial dimension imagine a safe with money in it. And someone grabs in through the 4th dimension and takes it. Imagine a flat-earther and his box, which would be a square drawn on the ground and that would be a solid barrier for him, he cannot get in. But you can take whatever is in there through the 3rd dimension without issues.
It might be our world has more than three dimensions. We would be flatlanders trying to understand the bouncy ball that creates some very strange phenomenon in our world.
Our brains are not made to understand higher spaces, but luckily, math allows us reach it with other means. In math there is nothing that stops us and opening more dimensions by just adding coordinates, for example "x, y, z, w, v" for "five dimensional space" and we can try to find calculations that explain what happens in our 3d-world.