1. **State the problem:** Simplify the expression $\frac{1}{4} \times \frac{5}{4}$.\n\n2. **Formula used:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}.$$\n\n3. **Apply the formula:** Multiply the numerators: $1 \times 5 = 5$.\nMultiply the denominators: $4 \times 4 = 16$.\nSo, $$\frac{1}{4} \times \frac{5}{4} = \frac{5}{16}.$$\n\n4. **Simplify if possible:** The fraction $\frac{5}{16}$ cannot be simplified further because 5 and 16 have no common factors other than 1.\n\n**Final answer:** $$\frac{5}{16}.$$