It's not zero. Zero can only be produced in adding or subtracting when two equal numbers with opposite signs are added or subtracted. -4 + 4 would give 0. Really tricky things like - 5 - (- 5) would be 0 because the 2 minus signs would give a plus.
-5 + 5 = 0
It's not positive either. Think money. If you owe someone 5 dollars and you put another 6 dollars on a credit card, your net worth isn't going up into the positive. It going down further into the negative. You wouldn't be alone. The US government does this every day. -5 - 6 = - 11
So - 1/3 - 4/5 is negative.
The answer is (though you haven't asked for it)
- 5/15 - 12/15 = - 17/15