jmc

Noticing that both 64 and 32 are powers of 2, we can rewrite the expression as ${\left(2^6\right)}^5={\left(2^5\right)}^x$. Simplifying, we get $$\begin{array}{rl}{\left(2^6\right)}^5& ={\left(2^5\right)}^x\\ 2^{6\cdot 5}& =2^{5\cdot x}\\ 2^{30}& =2^{5x}\\ 2^6& =2^x\\ 2^{-6}& =2^{-x}\end{array}$$ Thus, $2^{-6}=\frac{1}{2^6}=\boxed{\frac{1}{64}}$.