Which is correct = 5!, as Mr Cheetham says. Jack will explain. Perhaps Mr C should end his sentences with a full stop.

So 5!=1x2x3x4x5=120?

Harking back to my schooldays, you always do the multiplication or division sum first BEFORE attempting the addition or subtraction unless brackets are used, in which case the bit inside the bracket is calculated first, am I right? All of which would mean the answer is 5! or 120.

Why did I get mixed up in all of this?

I've only just noticed this thread - I think my machine was non compos mentis when it was posted.

I got quite indignant at first, until I noticed the twist. Very clever, bringing the mathematically knowledgeable down a peg.

Interesting philosophical point here, mixing maths and text!

This is not called up by the original expression, and is a misreading of the convention. Effectively, you have introduced it as a red herring. Of course, the rhs in the given expression would become:
(230-220)/2 = 5.
This solution is a non-starter, except for an eccentric.

The accepted general convention is as the second:

,
so the rhs becomes:
230 - (220/2) = 230-110 = 120, which is 5!

p.s. As this is a "nice" forum, it might be y's to mind our p's and q's!

William wrote:

This is quite irrelevant.

The clear intention of the original designer of the problem (I assume not the OP in this forum) was for readers who obeyed the standard process ("*/" then "+-") to evaluate the LHS, and be initially shocked by the statement that it was equal to a clearly incorrect number, not noticing the  "meta" addition of the factorial indicator. That is why I referred to the problem as being somewhat of a philosophical problem, a hybrid of text and maths.

I would like to introduce an analogy.
The adept mathematician understands how f', f'' etc. are used to represent dy/dx, d2y/d2x (you know what I mean- I don't know how to show superscript in this forum). This is an accepted shorthand, and no one would adapt or modify it. It has a meaning, which is universally understood.

I think, in the same way, the standard notation implies a process which is universally understood, where that notation is used. So if I write an expression using that notation, that is what I intend. If I meant to evaluate a "+-" function before a "*/" function, I would parse the expression in accordance.

The expansion of the expression in its correct and incorrect  formats may be interesting; a quick glance at the working shows interesting relationships - but it is an ephemera, a castle built on clay. It has nothing to do with the clever joke implied by the original maths expression in its text matrix.

BTW, another relationship, given
(P-Q)/2 =  n, and
P-Q/2 = n!
is:
n!/n = (n-1)! =
(P-Q/2)/(P/2-Q/2)
= (2P-Q)/(P-Q) = P/(P-Q)+(P-Q)/(P-Q)
=P/(P-Q) +1
So if n were 5, (5-1)! = 4! = 24,
and given the original expression, P=230, Q=220, and P/(P-Q) = 230/(230-220) =23, and adding the  +1, = 24
QED

If you are interested in the order of processes in an arithmetic "chain", try this 14 minute video. At least stick with the first half.
https://www.youtube.com/watch?v=eVRJLD0HJcE

At the end of the video, there is a most surprising conclusion. Worth a knowing chuckle!