1. **State the problem:** Simplify the expression $$2x^2(5x^5)$$. 2. **Apply the multiplication rule for exponents:** Multiply the coefficients and add the exponents of like bases. 3. Multiply the coefficients: $$2 \times 5 = 10$$. 4. Add the exponents for base $$x$$: $$2 + 5 = 7$$. 5. So, the expression simplifies to $$10x^7$$. **Final answer:** $$10x^7$$.