In solid state \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] exists as:
A) ${\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ - }{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ + }$
B) ${\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ - }{\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ + }$
C) ${\left[ {{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{4}}}} \right]^ - }{{\text{O}}^ + }$
D) $\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]$

Hint: To solve this we must know that \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is known as dinitrogen pentoxide. Dinitrogen pentoxide exists as a salt or ionic solid in solid state and thus, it contains separated cation and anion in its solid state. We have to identify the cation and anion.

Complete answer:
We know that \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is known as dinitrogen pentoxide. Dinitrogen pentoxide exists as a salt or ionic solid in solid state and thus, it contains separated cation and anions in its solid state. Dinitrogen pentoxide is solid at room temperature. A slight increase in temperature causes sublimation of dinitrogen pentoxide to a colourless gas.
We know that cation is a positively charged species whereas anion is a negatively charged species.
The compounds which consist of only two elements are known as binary compounds. Dinitrogen pentoxide contains only nitrogen and oxygen and thus, dinitrogen pentoxide belongs to a family of binary nitrogen oxides.
In solid state, the cation in dinitrogen pentoxide is the nitronium ion i.e. ${\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ + }$ and the anion in dinitrogen pentoxide is the nitrate ion i.e. ${\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ - }$. Thus, dinitrogen pentoxide is also known as nitronium nitrate.
The nitronium ion i.e. ${\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ + }$ has a linear structure whereas the nitrate ion i.e. ${\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ - }$ has a planar structure. The oxidation state of nitrogen in both nitronium ion and nitrate ion is $ + 5$.
Thus, in solid state \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] exists as ${\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ - }{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ + }$.
Thus, the correct option is (A) ${\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^ - }{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^ + }$.

Note:Dinitrogen pentoxide belongs to a family of binary nitrogen oxides. It is also known as nitric anhydride or nitryl nitrate or anhydrous nitric acid. Dinitrogen pentoxide exists as colourless crystals. Dinitrogen pentoxide is an unstable and potentially dangerous oxidiser.