How to find the empirical formula for an nitrogen oxygen compound from the given mass of nitrogen and the product?
$\ce{x/2 N2 +y/2 O2 \rightarrow N$_x$O$_y$}$

We have two unknowns $x$ and $y$. So, to determine them we need two independent  equations:

1 - The conservation of nitrogen mass: $5=14x$. So,  $x= 0.35714$.

2- According to the stoichiometry of the above balanced chemical equation: The number of moles of  $\ce{ N$_x$O$_y$}$ equals $n= \frac{5}{28}\times\frac{2}{x}$.

On the other hand, the number of moles of  $\ce{ N$_x$O$_y$}$ equals   $n= \frac{19.3}{14x+16y}=\frac{10}{28x} $.
By substituting $x= 0.35714 $ into the last equation, we find $y=0.89375$. 
We find $\ce{ N_{0.35714}O_{0.89375}}$. We divide by $ 0.35714$, We obtain  $\ce{ NO_{2.5}}$.i.e. the formula of nitrogen oxide is $\ce{ N_2O_5}$.