To find 5 rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$, let's proceed as follows:

Step 1: Represent the fractions with a common denominator.

The denominators of $\frac{3}{5}$ and $\frac{2}{3}$ are 5 and 3. The least common denominator (LCD) is 15.

$\frac{3}{5} = \frac{9}{15}, \quad \frac{2}{3} = \frac{10}{15}$

Now, we need to find 5 rational numbers between $\frac{9}{15}$ and $\frac{10}{15}$.

Step 2: Convert these fractions to equivalent fractions with a larger denominator.

For more options, let’s scale these fractions by multiplying numerator and denominator by 10:

$\frac{3}{5} = \frac{90}{150}, \quad \frac{2}{3} = \frac{100}{150}$

Thus, we need to find 5 rational numbers between $\frac{90}{150}$ and $\frac{100}{150}$.

Step 3: Choose rational numbers in the range.

Some examples of rational numbers are:

$\frac{91}{150}, \, \frac{92}{150}, \, \frac{93}{150}, \, \frac{94}{150}, \, \frac{95}{150}$

Step 4: Simplify these fractions (if needed).

The chosen numbers are already in their simplest forms and lie between $\frac{3}{5}$ and $\frac{2}{3}$.

Final Answer:

Five rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$ are:

$\frac{91}{150}, \quad \frac{92}{150}, \quad \frac{93}{150}, \quad \frac{94}{150}, \quad \frac{95}{150}.$

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Would you like further clarification or additional examples?
Here are five related questions:

1. What is the definition of rational numbers?
2. How can we find rational numbers between two integers?
3. Can you show steps to find rational numbers in decimal form?
4. What are irrational numbers and how do they differ from rational ones?
5. How can you confirm a fraction is in its simplest form?

Tip: To find rational numbers between two fractions, use a larger common denominator to create a finer "grid" of numbers in the interval.