1. **Problem:** Simplify the expression $x^5 \times x^7$ and find the value of $m$ such that $x^5 \times x^7 = x^m$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$x^a \times x^b = x^{a+b}$$ 3. **Apply the formula:** $$x^5 \times x^7 = x^{5+7} = x^{12}$$ 4. **Explanation:** Since the bases are the same ($x$), we add the exponents $5$ and $7$ to get $12$. 5. **Final answer:** $$m = 12$$