1. **State the problem:** Simplify the expression $$\frac{5ef \cdot y}{10ef - 5fg}$$. 2. **Identify the formula and rules:** We will factor the denominator and simplify the fraction by canceling common factors. 3. **Factor the denominator:** $$10ef - 5fg = 5(2ef - fg)$$ 4. **Rewrite the expression:** $$\frac{5ef \cdot y}{5(2ef - fg)}$$ 5. **Cancel the common factor 5:** $$\frac{ef \cdot y}{2ef - fg}$$ 6. **Final simplified expression:** $$\frac{efy}{2ef - fg}$$ This is the simplest form unless further factorization is possible based on variable relationships.