1. **State the problem:** Subtract the fractions $\frac{3}{8}$ and $\frac{1}{5}$. 2. **Formula:** To subtract fractions, use the formula $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$. 3. **Apply the formula:** Here, $a=3$, $b=8$, $c=1$, and $d=5$. So, $$\frac{3}{8} - \frac{1}{5} = \frac{3 \times 5 - 1 \times 8}{8 \times 5} = \frac{15 - 8}{40} = \frac{7}{40}.$$ 4. **Simplify:** The fraction $\frac{7}{40}$ cannot be simplified further because 7 and 40 have no common factors other than 1. 5. **Final answer:** $$\boxed{\frac{7}{40}}.$$