1. We are given the expression $5137 \times 65$, and we need to calculate its value. 2. Multiply the two numbers directly: $$5137 \times 65 = 5137 \times (60 + 5) = 5137 \times 60 + 5137 \times 5$$ 3. Calculate each part: $$5137 \times 60 = 308220$$ $$5137 \times 5 = 25685$$ 4. Add the results: $$308220 + 25685 = 333905$$ 5. Thus, the final answer is: $$\boxed{333905}$$