1. **State the problem:** Calculate $\frac{5}{7} - \frac{1}{4}$.\n\n2. **Formula and rules:** To subtract fractions, find a common denominator, then subtract the numerators.\n\n3. **Find common denominator:** The denominators are 7 and 4. The least common denominator (LCD) is $28$.\n\n4. **Convert fractions:**\n$$\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}$$\n$$\frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}$$\n\n5. **Subtract:**\n$$\frac{20}{28} - \frac{7}{28} = \frac{20 - 7}{28} = \frac{13}{28}$$\n\n6. **Final answer:**\n$$\frac{5}{7} - \frac{1}{4} = \frac{13}{28}$$