1. The problem is to evaluate the expression $(-11)^8 \times (-11)^5$. 2. We use the rule of exponents that states $a^m \times a^n = a^{m+n}$ when the bases are the same. 3. Here, the base is $-11$, and the exponents are 8 and 5. 4. Applying the rule: $$(-11)^8 \times (-11)^5 = (-11)^{8+5} = (-11)^{13}$$ 5. So the expression simplifies to $(-11)^{13}$. 6. Since 13 is an odd number, $(-11)^{13}$ is negative. 7. The exact value is $-11^{13}$, which is a very large negative number. Final answer: $$\boxed{(-11)^{13}}$$