Introduction:

Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. They can be positive, negative, or zero. In this question, we need to find five rational numbers between -5/7 and -3/8.

Method:

To find rational numbers between two given rational numbers, we can use the concept of averaging. We can find the average of the given numbers and use it as a reference point to find other rational numbers between them.

Step-by-step solution:

1. Convert the given rational numbers to a common denominator:
-5/7 = -40/56
-3/8 = -21/56

2. Find the average of the two given numbers:
Average = (-40/56 + -21/56) / 2 = -61/112

3. To find the first number between -5/7 and -3/8, take the average of -5/7 and -61/112:
Average = (-40/56 + -61/112) / 2 = -101/224

4. To find the second number between -5/7 and -3/8, take the average of -61/112 and -3/8:
Average = (-61/112 + -21/56) / 2 = -83/224

5. To find the third number between -5/7 and -3/8, take the average of -21/56 and -3/8:
Average = (-21/56 + -21/56) / 2 = -21/56

6. To find the fourth number between -5/7 and -3/8, take the average of -21/56 and -3/8:
Average = (-21/56 + -21/56) / 2 = -21/56

7. To find the fifth number between -5/7 and -3/8, take the average of -21/56 and -3/8:
Average = (-21/56 + -21/56) / 2 = -21/56

Conclusion:

The five rational numbers between -5/7 and -3/8 are:
-101/224, -83/224, -21/56, -21/56, -21/56.