1. **Stating the problem:** Two brothers are currently 5 and 8 years old. We want to find in how many years their ages will be in the ratio 4:5. 2. **Formula and explanation:** Let the number of years after which their ages are in ratio 4:5 be $x$. After $x$ years, the ages will be $5 + x$ and $8 + x$. The ratio condition is: $$\frac{5 + x}{8 + x} = \frac{4}{5}$$ 3. **Solving the equation:** Cross-multiply: $$5(5 + x) = 4(8 + x)$$ Simplify: $$25 + 5x = 32 + 4x$$ Subtract $4x$ from both sides: $$25 + x = 32$$ Subtract 25 from both sides: $$x = 7$$ 4. **Answer:** In 7 years, their ages will be in the ratio 4:5. --- **Another similar question:** Two sisters are currently 6 and 9 years old. In how many years will their ages be in the ratio 5:7?