1. **State the problem:** Simplify the expression $\frac{5 \times 70 - 50}{10}$. 2. **Apply the order of operations:** First, multiply $5$ by $70$. $$5 \times 70 = 350$$ 3. **Substitute back into the expression:** $$\frac{350 - 50}{10}$$ 4. **Perform the subtraction in the numerator:** $$350 - 50 = 300$$ 5. **Rewrite the expression:** $$\frac{300}{10}$$ 6. **Simplify the fraction by dividing numerator and denominator by 10:** $$\frac{\cancel{300}^{30}}{\cancel{10}^{1}} = 30$$ 7. **Final answer:** $$30$$