1. **State the problem:** Simplify the expression $$5 - \frac{5}{12} - \frac{5}{28} \times 0.7$$. 2. **Recall the order of operations:** Multiplication comes before subtraction. 3. **Calculate the multiplication first:** $$\frac{5}{28} \times 0.7 = \frac{5}{28} \times \frac{7}{10} = \frac{5 \times 7}{28 \times 10} = \frac{35}{280}$$ 4. **Simplify the fraction:** $$\frac{35}{280} = \frac{\cancel{35}^7}{\cancel{280}^56} = \frac{7}{56}$$ 5. **Rewrite the expression:** $$5 - \frac{5}{12} - \frac{7}{56}$$ 6. **Find a common denominator for the fractions:** The denominators are 12 and 56. The least common denominator (LCD) is 168. 7. **Convert fractions to have denominator 168:** $$\frac{5}{12} = \frac{5 \times 14}{12 \times 14} = \frac{70}{168}$$ $$\frac{7}{56} = \frac{7 \times 3}{56 \times 3} = \frac{21}{168}$$ 8. **Rewrite the expression with common denominators:** $$5 - \frac{70}{168} - \frac{21}{168}$$ 9. **Convert 5 to a fraction with denominator 168:** $$5 = \frac{5 \times 168}{168} = \frac{840}{168}$$ 10. **Perform the subtraction:** $$\frac{840}{168} - \frac{70}{168} - \frac{21}{168} = \frac{840 - 70 - 21}{168} = \frac{749}{168}$$ 11. **Simplify if possible:** 749 and 168 have no common factors other than 1, so the fraction is in simplest form. **Final answer:** $$\boxed{\frac{749}{168}}$$