how many times is each basic property of associative commutative and distributive used to evaluate the expression 23 + 5x + 7y - x - 5 - 27 respectively

This is a goofy question, because the method of counting is not very well defined.

23 + 5x + 7y - x - 5 - 27

Let's make everything an addition because addition is associative but subtraction isn't.

= 23 + 5x + 7y + - x + - 5 + - 27

OK, let's commute a few things

= 5x + 7y + - x + - 5 + - 27 + 23

= 5x + - x + 7y + - 5 + - 27 + 23

That's two commutations.

= (5x + - x) + 7y + ((-5 + - 27) + 23)

I'll count that as three associations

= (5 + - 1) x + 7y + - 9

That's a distributive law (in reverse which is fine)

= 4x + 7y - 9

Tallying that's associative law 3 times, commutative law 2 times, distributive law 1 time.