smc

We can rewrite $10^x\cdot 100^{2x}=1000^5$ as $10^{5x}=10^{15}$: $$\begin{array}{rl}10^x\cdot 100^{2x}& =10^x\cdot (10^2{)}^{2x}\\ 10^x\cdot 10^{4x}& =(10^3{)}^5\\ 10^{5x}& =10^{15}\end{array}$$ Since the bases are equal, we can set the exponents equal, giving us $5x=15$. Solving the equation gives us $x=\boxed{3}.$