1. **State the problem:** Simplify the expression $5(27 \div 34)2$. 2. **Recall the order of operations:** Perform division and multiplication from left to right. 3. **Calculate the division first:** $$27 \div 34 = \frac{27}{34}$$ 4. **Rewrite the expression:** $$5 \times \frac{27}{34} \times 2$$ 5. **Multiply the numbers:** $$5 \times 2 = 10$$ 6. **Now multiply:** $$10 \times \frac{27}{34} = \frac{10 \times 27}{34} = \frac{270}{34}$$ 7. **Simplify the fraction:** Both numerator and denominator can be divided by 2: $$\frac{270 \div 2}{34 \div 2} = \frac{135}{17}$$ **Final answer:** $$\frac{135}{17}$$