1. **Problem:** Find $x$ such that $$(-5)^{x+1} \times (-5)^5 = (-5)^7.$$ 2. **Formula and rules:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}.$$ 3. **Apply the rule:** $$(-5)^{x+1} \times (-5)^5 = (-5)^{(x+1)+5} = (-5)^{x+6}.$$ 4. **Set equal to the right side:** $$(-5)^{x+6} = (-5)^7.$$ 5. **Since the bases are equal and nonzero, equate exponents:** $$x+6 = 7.$$ 6. **Solve for $x$:** $$x = 7 - 6 = 1.$$ **Final answer:** $$x = 1.$$