1. **State the problem:** Simplify the expression $\left(5 \frac{7}{3}\right) \times \left(5 \frac{8}{3}\right)$ and express it in the form $5k$ where $k$ is a number. 2. **Convert mixed numbers to improper fractions:** - $5 \frac{7}{3} = 5 + \frac{7}{3} = \frac{15}{3} + \frac{7}{3} = \frac{22}{3}$ - $5 \frac{8}{3} = 5 + \frac{8}{3} = \frac{15}{3} + \frac{8}{3} = \frac{23}{3}$ 3. **Multiply the two improper fractions:** $$\frac{22}{3} \times \frac{23}{3} = \frac{22 \times 23}{3 \times 3} = \frac{506}{9}$$ 4. **Express the result as $5k$:** We want to write $\frac{506}{9} = 5k$, so solve for $k$: $$k = \frac{506}{9 \times 5} = \frac{506}{45}$$ 5. **Final answer:** $$\left(5 \frac{7}{3}\right) \times \left(5 \frac{8}{3}\right) = 5 \times \frac{506}{45}$$ Thus, $k = \frac{506}{45}$.