1. **State the problem:** Calculate the value of the expression $$80 \div \left(4^2 \div \frac{2}{5}\right) + 3.75$$. 2. **Recall the order of operations:** Parentheses first, then exponents, then division and multiplication from left to right, and finally addition. 3. **Calculate the exponent:** $$4^2 = 16$$. 4. **Rewrite the expression inside the parentheses:** $$16 \div \frac{2}{5}$$. 5. **Divide by a fraction by multiplying by its reciprocal:** $$16 \times \frac{5}{2}$$. 6. **Calculate the multiplication:** $$16 \times \frac{5}{2} = \cancel{16} \times \frac{5}{\cancel{2}} = 8 \times 5 = 40$$. 7. **Now the expression is:** $$80 \div 40 + 3.75$$. 8. **Divide:** $$80 \div 40 = 2$$. 9. **Add:** $$2 + 3.75 = 5.75$$. **Final answer:** $$5.75$$