1. Stating the problem: Simplify the expression $$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{2}{5}\right)^3 + \left(\frac{3}{5}\right)^5 \times \left(\frac{3}{5}\right)^{-5}.$$\n\n2. Formula and rules: When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}.$$ Also, any number raised to the zero power equals 1: $$a^0 = 1.$$\n\n3. Apply the rule to the first term: $$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{2}{5}\right)^3 = \left(\frac{2}{5}\right)^{-3+3} = \left(\frac{2}{5}\right)^0 = 1.$$\n\n4. Apply the rule to the second term: $$\left(\frac{3}{5}\right)^5 \times \left(\frac{3}{5}\right)^{-5} = \left(\frac{3}{5}\right)^{5 + (-5)} = \left(\frac{3}{5}\right)^0 = 1.$$\n\n5. Add the simplified terms: $$1 + 1 = 2.$$\n\nFinal answer: $$2.$$