1. **State the problem:** Solve for $x$ in the equation $\frac{5}{1} \times \frac{x}{5} = 35 \times 5$. 2. **Write the equation clearly:** $$\frac{5}{1} \times \frac{x}{5} = 35 \times 5$$ 3. **Simplify the right side:** $$35 \times 5 = 175$$ 4. **Multiply the fractions on the left side:** $$\frac{5 \times x}{1 \times 5} = \frac{5x}{5}$$ 5. **Cancel common factors:** $$\frac{\cancel{5}x}{\cancel{5}} = x$$ 6. **So the equation reduces to:** $$x = 175$$ 7. **Final answer:** $$\boxed{175}$$