1. **State the problem:** We are given the area of a triangle as $\frac{25}{3}$ square centimeters and the height as $\frac{2}{5}$ cm. We need to find the length of the base expressed as a fraction in simplest form. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Substitute the known values:** $$\frac{25}{3} = \frac{1}{2} \times \text{base} \times \frac{2}{5}$$ 4. **Simplify the right side:** $$\frac{1}{2} \times \frac{2}{5} = \frac{\cancel{2}}{2} \times \frac{1}{5} = \frac{1}{5}$$ So, $$\frac{25}{3} = \text{base} \times \frac{1}{5}$$ 5. **Solve for the base:** Multiply both sides by 5: $$\text{base} = \frac{25}{3} \times 5 = \frac{25 \times 5}{3} = \frac{125}{3}$$ 6. **Final answer:** The length of the base is $$\boxed{\frac{125}{3}}$$ centimeters.