1. **State the problem:** Calculate the value of $2 \times 5^2$. 2. **Recall the order of operations:** Exponents are evaluated before multiplication. 3. **Evaluate the exponent:** $$5^2 = 5 \times 5 = 25$$ 4. **Multiply the result by 2:** $$2 \times 25 = 50$$ 5. **Final answer:** $$\boxed{50}$$