1. **State the problem:** Simplify the expression $$\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$$. 2. **Recall the formula:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}} = \frac{1}{k+2} \times \frac{k^2-4}{5}$$. 3. **Factor the difference of squares:** Note that $$k^2 - 4 = (k+2)(k-2)$$. 4. **Substitute the factorization:** $$\frac{1}{k+2} \times \frac{(k+2)(k-2)}{5}$$. 5. **Cancel common factors:** The factor $$k+2$$ appears in numerator and denominator, so $$\frac{1}{\cancel{k+2}} \times \frac{\cancel{k+2}(k-2)}{5} = \frac{k-2}{5}$$. 6. **Final simplified expression:** $$\boxed{\frac{k-2}{5}}$$. This matches the answer choice $$\frac{k-2}{5}$$. **Answer:** $$\frac{k-2}{5}$$.