1. The problem is to subtract the mixed numbers $5 \frac{2}{3}$ and $3 \frac{3}{4}$. 2. First, convert the mixed numbers to improper fractions. For $5 \frac{2}{3}$: $$5 \times 3 + 2 = 15 + 2 = 17$$ so it becomes $$\frac{17}{3}$$. For $3 \frac{3}{4}$: $$3 \times 4 + 3 = 12 + 3 = 15$$ so it becomes $$\frac{15}{4}$$. 3. To subtract $$\frac{17}{3} - \frac{15}{4}$$, find a common denominator. The least common denominator of 3 and 4 is 12. 4. Convert each fraction to have denominator 12: $$\frac{17}{3} = \frac{17 \times 4}{3 \times 4} = \frac{68}{12}$$ $$\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}$$ 5. Now subtract the numerators: $$\frac{68}{12} - \frac{45}{12} = \frac{68 - 45}{12} = \frac{23}{12}$$ 6. Convert the improper fraction back to a mixed number: $$\frac{23}{12} = 1 \frac{11}{12}$$ because $23 \div 12 = 1$ remainder $11$. 7. Therefore, the final answer is $1 \frac{11}{12}$.