Think of the order of operations as equivalent to punctuation and grammar.
If you follow "official grammar, then "I ain't no fool" means that you are saying you are a fool. There's a double negative. Unofficial grammar will lead to the opposite interpretation.
Now, which interpretation of the sentence is "correct"? Well, the correct interpretation is whatever the speaker actually meant to say.
That's where the trouble begins with BIDMAS. While it is very broadly accepted as the "correct way" to write mathematics and while it does have some benefits, the correct interpretation of an equation is what the writer intended to write. If you are writing mathematics you should do what you can to make your intentions clear.
Please know that many people disagree with my opinion on this, but I would argue that, when devoid of any of context, the expression
Is meaningless. It is EASILY interpreted as (5+7)x3 OR 5+(7x3). BIDMAS will ensure that most people will interpret the expression as the later, but the former interpretation is by no means unreasonable.
In scenario's like this, I try to include brackets, to ensure that people don't even need to consider BIDMAS. My intended meaning should be the first thing that comes to any readers mind. Just like when I am speaking, I am careful to word the sentence so that my meaning is clear.
This does not mean that you need to over whelm of your maths with a million parentheses. Just as it does not mean that you should write sentences with loads of punctuation and clarifying statements. There is clearly a healthy balance between brevity and clarity.
You'd be hard pressed to see 3 + 5y and think that it means (3+5)y. But 3+5x7 is less obvious and it costs you nothing to write 3+(5x7) or 3+5(7) to make the intended meaning clear despite the readers familiarity with BIDMAS.
I (like most mathematicians) understand BIDMAS, but even I find 3+5(7) more pleasant to read than 3+5x7.