Kiley had a piece of bamboo skewer that measured 14Three-fifths inches long. She wanted to cut it into toothpicks that were each 3One-fifth inches long. How many toothpicks can she make?

To determine how many toothpicks Kiley can make, we need to divide the total length of the bamboo skewer by the length of each toothpick.

1. **Convert the mixed numbers to improper fractions:**
- For \( 14\frac{3}{5} \):
\[
14\frac{3}{5} = \frac{14 \times 5 + 3}{5} = \frac{70 + 3}{5} = \frac{73}{5}
\]
- For \( 3\frac{1}{5} \):
\[
3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}
\]

2. **Divide the total length by the length of each toothpick:**
\[
\text{Number of toothpicks} = \frac{14\frac{3}{5}}{3\frac{1}{5}} = \frac{\frac{73}{5}}{\frac{16}{5}}
\]

3. **Dividing fractions (multiply by the reciprocal):**
\[
= \frac{73}{5} \times \frac{5}{16} = \frac{73 \times 5}{5 \times 16} = \frac{73}{16}
\]

4. **Calculate \( 73 \div 16 \):**
- To find how many whole toothpicks she can make, divide 73 by 16.
\[
73 \div 16 = 4.5625
\]
This means Kiley can make 4 whole toothpicks since we only take the whole part.

Thus, Kiley can make **4 toothpicks**.