1. **State the problem:** Sarah is 5 years older than her brother, and the sum of their ages is 35 years. 2. **Define variables:** Let $x$ represent her brother's age. 3. **Express Sarah's age:** Since Sarah is 5 years older, her age is $x + 5$. 4. **Write the equation:** The sum of their ages is 35, so: $$x + (x + 5) = 35$$ 5. **Simplify the equation:** $$2x + 5 = 35$$ 6. **Isolate $x$:** Subtract 5 from both sides: $$2x + \cancel{5} - \cancel{5} = 35 - 5$$ $$2x = 30$$ 7. **Solve for $x$:** Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{30}{\cancel{2}}$$ $$x = 15$$ 8. **Find Sarah's age:** $$x + 5 = 15 + 5 = 20$$ **Final answers:** - Brother's age: 15 - Sarah's age: 20