For $Br{O_2} \to B{r^ - }$, the relation between normality and molarity is given as $N = M \times x$, value of $x$ is:

Hint - For some chemical solutions, Normality and Molarity are equivalent or N=M. This generally occurs when N=1. The process of converting molarity to normality matters only when the number of equivalents change by the level of ionization. Here, basicity refers to the number of H+ ions that can be given by an acid molecule.

Complete step by step answer:
While Molarity refers to the concentration of a compound or ion in any solution, normality refers to the molar concentration only of the acid or only of base component in the solution. So, the normality in acid-base reactions has a much deeper understanding of the solution's concentration.
n-factor can be defined as the number of OH– ions displaced by 1 mole of base in any reaction. Note that n-factor is not equal to its acidity because the number of moles that are replaceable OH– ions present in 1 mole of base.
We calculate the n factor by finding the change in oxidation state in any reaction:
In,
 $Br{O_2}\, \to \,B{r^ - } \\
\downarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \\
+ 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 1 \\
$Change in oxidation state=4-(-1)
 =5
As we know,
Normality = Molarity $\times$ n− factor
= $M \times 5$
Therefore, the value of n-factor is 5.
Thus the value of x is 5.

Note - Acids are the species which releases ${H^ + }$ ion, when dissolved in solvent. For them, n-factor is determined as the number of ${H^ + }$ ions released by 1 mole of acid in a reaction. The n- factor for acid is $ \ne $ its basicity. When we talk about bases, they are the species, which release $O{H^ - }$ion when dissolved in solvent. For bases n- factor is determined as the number of $O{H^ - }$ ions released by 1 mole of base in a reaction, n-factor is $ \ne $ its acidity.