1. **State the problem:** Simplify the expression $$\frac{5}{(r+4)(r-7)} \times \frac{r-7}{r+6}$$ as a single fraction in simplest form. 2. **Write the expression:** $$\frac{5}{(r+4)(r-7)} \times \frac{r-7}{r+6}$$ 3. **Multiply the numerators and denominators:** $$\frac{5 \times (r-7)}{(r+4)(r-7) \times (r+6)}$$ 4. **Cancel common factors:** The factor $(r-7)$ appears in both numerator and denominator, so it cancels out: $$\frac{5}{(r+4)(r+6)}$$ 5. **Final simplified fraction:** $$\frac{5}{(r+4)(r+6)}$$ This is the expression in its simplest form because no further factorization or cancellation is possible.