Answer
7 dB.
Work Step by Step
The first person is a distance of $r_1=100\;m$ from the explosion, while the second person is a distance $r_2=\sqrt{5}(100\;m)$ from the explosion.
The sound intensity is inversely proportional to the square of the distance from the source.
$$\frac{I_1}{I_2}=\frac{r_2^2}{r_1^2}=5$$
Use the definition of sound level. The change in sound level depends logarithmically on the increase in intensity.
$$\beta = 10log \frac{I_1}{I_2}=10log 5\approx 7\;dB$$
