1. **State the problem:** We need to find the 10th term of a geometric sequence where the first term $a_1 = -5$ and the common ratio $r = -2$. 2. **Formula for the $n^{th}$ term of a geometric sequence:** $$a_n = a_1 \times r^{n-1}$$ This formula means to find the $n^{th}$ term, multiply the first term by the common ratio raised to the power of $n-1$. 3. **Apply the formula for the 10th term:** $$a_{10} = -5 \times (-2)^{10-1} = -5 \times (-2)^9$$ 4. **Calculate $(-2)^9$:** Since $(-2)^9 = -2 \times (-2)^8$ and $(-2)^8 = 256$, then $$(-2)^9 = -2 \times 256 = -512$$ 5. **Substitute back:** $$a_{10} = -5 \times (-512)$$ 6. **Multiply:** $$a_{10} = -5 \times (-512) = 2560$$ 7. **Answer:** The 10th term of the sequence is **2560**. Therefore, the correct choice is **b. 2560**.