What number is less than - 2 4/5 and greater than - 31/5

Using a calculator, you should find that

-2 & 4/5 = - (2 + 4/5) = - (2+0.8) = - 2.8

-31/5 = - 6.2

So the unknown number is between - 6.2 and - 2.8

Possible whole number answers could be: - 6, - 5, - 4, - 3, or - 2

If your teacher allows decimal answers, then there are infinitely many possible ways to answer.