An atmospheric inversion has taken place such that the temperature at the surface is $5^{\circ} \mathrm{C}$ while the temperature at $4,000 \mathrm{~m}$ is a balmy $20^{\circ} \mathrm{C}$. Assuming a linear temperature drop over that distance and a barometric pressure of $750 \mathrm{~mm} \mathrm{Hg}$ at the surface, what is the pressure at $4,000 \mathrm{~m}$ ?