1. **State the problem:** Evaluate the expression $$5 + \frac{3}{5 + \frac{3}{5 - 3}}$$. 2. **Understand the structure:** This is a nested fraction (a complex fraction) where the denominator itself contains a fraction. 3. **Start from the innermost expression:** Calculate $$5 - 3$$. $$5 - 3 = 2$$ 4. **Substitute back:** The expression becomes $$5 + \frac{3}{5 + \frac{3}{2}}$$ 5. **Calculate the denominator of the denominator:** $$5 + \frac{3}{2} = \frac{10}{2} + \frac{3}{2} = \frac{13}{2}$$ 6. **Rewrite the expression:** $$5 + \frac{3}{\frac{13}{2}}$$ 7. **Divide by a fraction:** Dividing by $$\frac{13}{2}$$ is the same as multiplying by its reciprocal: $$\frac{3}{\frac{13}{2}} = 3 \times \frac{2}{13} = \frac{6}{13}$$ 8. **Add to 5:** $$5 + \frac{6}{13} = \frac{65}{13} + \frac{6}{13} = \frac{71}{13}$$ 9. **Final answer:** $$\boxed{\frac{71}{13}}$$ This fraction is approximately 5.46, which does not match any of the given options A) 5, B) 3, C) 2, D) 1/5, E) 2/12 exactly, so the exact simplified answer is $$\frac{71}{13}$$.