Explanation:

To determine the number of rational numbers that lie between 1/5 and 1/3, we need to find the rational numbers with denominators between 5 and 3.

Finding the Rational Numbers:
To find the rational numbers between 1/5 and 1/3, we need to find the fractions with denominators between 5 and 3.

Finding the Smallest Rational Number:
The smallest rational number that lies between 1/5 and 1/3 can be found by taking the average of the two given numbers.

Average = (1/5 + 1/3) / 2 = 8/30 = 4/15

So, the smallest rational number that lies between 1/5 and 1/3 is 4/15.

Finding the Largest Rational Number:
The largest rational number that lies between 1/5 and 1/3 can be found by taking the average of the two given numbers.

Average = (1/5 + 1/3) / 2 = 8/30 = 4/15

So, the largest rational number that lies between 1/5 and 1/3 is also 4/15.

Finding the Number of Rational Numbers:
Since the smallest and largest rational numbers between 1/5 and 1/3 are the same, it means that there is an infinite number of rational numbers between 1/5 and 1/3.

This is because we can always find a rational number that lies between any two rational numbers by taking their average. In this case, the average is the same for both the smallest and largest rational numbers, which means there are infinitely many rational numbers between them.

Therefore, the correct answer is option 'D' - Infinite numbers.