To simplify the expression, we need to combine the exponents. When we multiply powers with the same base, we add the exponents: $13^{-5} \cdot 13^{-11} = 13^{(-5)+(-11)} = 13^{-16}$. To get an equivalent expression with only positive exponents, we can replace $13^{-16}$ with its reciprocal, $1/13^{16}$. Therefore, the answer is $\boxed{\text{(C)}\ 1/13^{16}}$.
