1. **State the problem:** We want to simplify the expression $5\left(\frac{2}{3}\right) \div 4$. 2. **Recall the division rule:** Dividing by a number is the same as multiplying by its reciprocal. So, dividing by 4 is the same as multiplying by $\frac{1}{4}$. 3. **Rewrite the expression:** $$5\left(\frac{2}{3}\right) \div 4 = 5\left(\frac{2}{3}\right) \times \frac{1}{4}$$ 4. **Multiply the numerators and denominators:** $$= \frac{5 \times 2}{3} \times \frac{1}{4} = \frac{10}{3} \times \frac{1}{4}$$ 5. **Multiply the fractions:** $$= \frac{10 \times 1}{3 \times 4} = \frac{10}{12}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (2):** $$= \frac{\cancel{10}^{\,5}}{\cancel{12}^{\,6}}$$ 7. **Final simplified answer:** $$\frac{5}{6}$$ So, the expression simplifies to $\frac{5}{6}$.