1. The problem asks to find the distance between the centers of two circles with radii 5 cm and 8 cm, respectively. 2. When two circles are tangent externally, the distance between their centers equals the sum of their radii. 3. When two circles are tangent internally, the distance between their centers equals the difference of their radii. 4. Since the problem mentions "expenses" (interpreted as tangency), we consider both cases: - External tangency distance: $$d = 5 + 8 = 13\text{ cm}$$ - Internal tangency distance: $$d = 8 - 5 = 3\text{ cm}$$ 5. Therefore, the distance between the centers of the two circles can be either 13 cm (external tangency) or 3 cm (internal tangency), depending on how the circles touch. Final answer: The distance between the centers is either $$3\text{ cm}$$ or $$13\text{ cm}$$.