Let  $X=\{1,2,3,4,5\},$  the number of different ordered pairs  $(Y,Z)$  that can be formed such that $Y\subseteq X,Z\subseteq X$   and $Y\cap Z$ is empty, is

$X=\{1,2,3,4,5\}$ ,  Y,Z are  two sets
 $$\begin{gathered} 1\in Y,1\in Z,\text{\hspace{0.17em}\hspace{0.17em}Y}\cap Z\ne \varphi \\ 1\in Y,1\notin Z,Y\cap Z=\varphi \\ 1\notin Y,1\in Z,Y\cap Z=\varphi \\ 1\notin Y,1\notin Z,Y\cap Z=\varphi \end{gathered}$$
 Similarly 2,3,4,5 each contains 3 possibilities 
Required no.of ordered pairs= $3\times 3\times 3\times 3\times 3=3^5$