1. **State the problem:** We are given that the ratio of one side of triangle ABC to the corresponding side of triangle DEF is $5:8$, and the perimeter of triangle DEF is 96 inches. We need to find the perimeter of triangle ABC. 2. **Formula used:** The perimeters of similar triangles are proportional to the lengths of their corresponding sides. So, $$\frac{\text{Perimeter of } ABC}{\text{Perimeter of } DEF} = \frac{5}{8}$$ 3. **Apply the formula:** Let the perimeter of ABC be $P$. Then, $$\frac{P}{96} = \frac{5}{8}$$ 4. **Solve for $P$:** Multiply both sides by 96: $$P = 96 \times \frac{5}{8}$$ 5. **Simplify the multiplication:** $$P = 96 \times \frac{5}{8} = \cancel{96} \times \frac{5}{\cancel{8}} = 12 \times 5 = 60$$ 6. **Conclusion:** The perimeter of triangle ABC is 60 inches.