How does commutative property not hold for subtraction?

Question

I don't get why commutative property is not valid under subtraction, because I find that it is for example: $5 - 3 = 2 = -3 + 5$ or rather $5 + (-3) = 2 = -3 + 5$ So how does it not hold true for negative numbers?

Answer 1

That is not the commutative property. If subtraction were commutative, what would mean that for any $a,b$; $$a - b = b - a$$ and this is clearly not the case, for example take $a=1$ and $b=2$

Answer 2

Addition is commutative: $$a+b=b+a$$ This holds for any numbers $a,b$, e.g. $a=5$ and $b=-3$, as in your example.

Subtraction is not (always) commutative: $$a-b\neq b-a$$ for most $a,b$ (not if $a=b$).

E.g. $5-3=2\neq-2=3-5$.