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 the 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. **Solve for $x$:** Subtract 5 from both sides: $$2x + \cancel{5} - \cancel{5} = 35 - 5$$ $$2x = 30$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{30}{\cancel{2}}$$ $$x = 15$$ 7. **Find Sarah's age:** $$x + 5 = 15 + 5 = 20$$ **Final answer:** - Brother's age is $15$ years. - Sarah's age is $20$ years.