1. **State the problem:** We need to add the mixed numbers $5 \frac{8}{4}$ and $4 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:** $5 \frac{8}{4} = 5 + \frac{8}{4} = 5 + 2 = 7$ because $\frac{8}{4} = 2$. $4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}$. 3. **Add the numbers:** $7 + \frac{13}{3} = \frac{7 \times 3}{3} + \frac{13}{3} = \frac{21}{3} + \frac{13}{3} = \frac{21 + 13}{3} = \frac{34}{3}$. 4. **Convert the improper fraction back to a mixed number:** $\frac{34}{3} = 11 \frac{1}{3}$ because $34 \div 3 = 11$ remainder $1$. **Final answer:** $$11 \frac{1}{3}$$