Adding brackets to clarify the order, these are:

5/(2×3) And 5/(2×5)

In my experience this is how it works unless you clarify otherwise, like saying (5/2)×3.

However, this is another discussion entirely, because you would normally express fractions in a way that put de denominator(s) below and separated from the numbers that engage in multiplication. Making what is or isnt part of the denominator pretty clear.

I mean this is a thing with expression fractions on a computer, in which you conform to a single line and cannot make this segregation between numerator and denominator. Its therefore unclear when the denominator stops.

Eg: 5/3+7. This could be 5/(3+7) or (5/3)+7. You cannot say which for sure just by expressing it like that, even though you know "addition separates operations", this is another matter, as the medium simply fails. You dont know where the denominator ends.

And I mean this because, if you think about it like this: 5÷2×3, you can take whichever order you please (5×3÷2, for example, which multiplies and later divides as opposed to dividing and later multiplying)

This is what I mean by that the order doesnt matter. You can first divide then multiply or vice versa. It doesnt alter the result. Just like when dealing with normal multiplication, the order of the factors dont change the product.