[tex]\bf 10^x\cdot 10^{2x}=1000^5\qquad \boxed{1000=10^3}\qquad 10^x\cdot 10^{2x}=(10^3)^5
\\\\\\
10^{x+2x}=10^{3\cdot 5}\implies 10^{3x}=10^{15}\impliedby
\begin{array}{llll}
\textit{the bases are the same, thus}\\
\textit{exponents must also}\\
\textit{be the same}
\end{array}
\\\\\\
3x=15\implies x=\cfrac{15}{3}\implies x=5[/tex]
