1. **State the problem:** Find the sum of the fractions $\frac{1}{5}$, $\frac{2}{3}$, $\frac{3}{5}$, and $\frac{1}{3}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. The sum is given by $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ when denominators differ.\n\n3. **Find the common denominator:** The denominators are 5 and 3. The least common denominator (LCD) is $15$.\n\n4. **Convert each fraction to have denominator 15:**\n$$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$$\n$$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$$\n$$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$$\n$$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$\n\n5. **Add the numerators:**\n$$\frac{3}{15} + \frac{10}{15} + \frac{9}{15} + \frac{5}{15} = \frac{3 + 10 + 9 + 5}{15} = \frac{27}{15}$$\n\n6. **Simplify the fraction:**\n$$\frac{27}{15} = \frac{\cancel{3} \times 9}{\cancel{3} \times 5} = \frac{9}{5}$$\n\n7. **Final answer:** The sum is $\frac{9}{5}$ or $1 \frac{4}{5}$.