Answer
$\theta_5 = 56.9^{\circ}$
Work Step by Step
Note that a reflected ray has the same angle as an incident ray. By geometry, the incident ray at the boundary between material 1 and the air is $\theta_1 = 40.1^{\circ}$
According to Snell's law:
$n_a~sin~\theta_5 = n_1~sin~\theta_1$
$n_a$ is the index of refraction in air
$\theta_5$ is the refracted angle in air
We can find $\theta_a$:
$n_a~sin~\theta_5 = n_1~sin~\theta_1$
$sin~\theta_5 = \frac{n_1~sin~\theta_1}{n_a}$
$\theta_5 = sin^{-1}~(\frac{n_1~sin~\theta_1}{n_a})$
$\theta_5 = sin^{-1}~(\frac{1.30~sin~40.1^{\circ}}{1.00})$
$\theta_5 = sin^{-1}~(0.83736)$
$\theta_5 = 56.9^{\circ}$
