Passage: Two volatile liquids A and B form an ideal solution....

Passage: Two volatile liquids A and B form an ideal solution. Consider a $5$ molal solution of B in A inside a closed container having a total vapour pressure of $100$ mm Hg at $300$ K. The vapour pressure of pure A at $300$ K is $105$ mm Hg. Assume that A and B behave as ideal gases in the vapour phase.
Given:
The gas constant $R = 0.08$ L atm K$^{-1}$ mol$^{-1}$
Molar mass of A is $50$ g mol$^{-1}$
Molar mass of B is $57$ g mol$^{-1}$
Density of liquid B at $300$ K is $0.5$ g/mL
$1$ atm $= 760$ mm Hg

Question: The mole fraction of B in vapour phase which is in equilibrium with this solution is ____.