$\begin{array}{l}\text{Here,}\\ \Rightarrow {\text{ (4)}}^{\text{?}}\text{= 1024}\\ \\ \Rightarrow {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(4)}}^{\text{4}}{\text{= 2}}^{\text{10}}\\ \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}[1024=2}\times \text{2}\times \text{2 }....\text{ 10 times]}\\ \\ \text{Now, \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\left(2^2\right)}^{?}{\text{\hspace{0.17em}= 2}}^{\text{10}}\\ \\ \Rightarrow {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} 2}}^{\text{2x?}}{\text{=2}}^{\text{10}}[\because {\text{2}}^{\text{2}\times \text{?}}=2^{2\times ?}]\\ \\ \Rightarrow 2\times ?=10\Rightarrow ?=5\end{array}$

Hence, Option E is correct.