Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In this case, we are looking for five rational numbers between -1 and 0. Let's explore some options:

1. -3/4: This rational number is between -1 and 0 because -3/4 is smaller than -1 but greater than 0. We can see this by comparing -3/4 with -1. Since -3/4 is closer to 0 than -1, it lies between these two numbers.

2. -2/3: Similarly, -2/3 is a rational number between -1 and 0. By comparing -2/3 with -1, we can see that -2/3 is closer to 0 than -1, so it lies between these two numbers.

3. -1/2: Another rational number between -1 and 0 is -1/2. By comparing -1/2 with -1, we can see that -1/2 is closer to 0 than -1, so it lies between these two numbers.

4. -1/3: -1/3 is also a rational number between -1 and 0. By comparing -1/3 with -1, we can see that -1/3 is closer to 0 than -1, so it lies between these two numbers.

5. -1/4: Finally, -1/4 is a rational number between -1 and 0. By comparing -1/4 with -1, we can see that -1/4 is closer to 0 than -1, so it lies between these two numbers.

In summary, the five rational numbers between -1 and 0 are -3/4, -2/3, -1/2, -1/3, and -1/4. We determined this by comparing the fractions with -1 and 0 and finding the fractions that are closer to 0 than -1.