Let's denote the person standing due south as S and the one standing due west as W. Also, let the tower be at point T. From person S's perspective, we have a right triangle $\triangle SPT$. The height of the tower PT is given as 5m, which is the opposite side for angle S. The angle at S is $45^\circ$. From the tangent trigonometric ratio, we have : $\tan{45^\circ} = \frac{PT}{ST} = \frac{5}{ST}$ Since $\tan{45^\circ}=1$, we get $ST = 5$m. Similarly, from person W's perspective, we have a right triangle $\triangle WPT$. The angle at W is $30^\circ$. From the tangent trigonometric ratio, we have: $\tan{30^\circ} = \frac{PT}{WT} = \frac{5}{WT}$ Since $\tan{30^\circ}=\frac{1}{\sqrt{3}}$, we get $WT = 5\sqrt{3}$m. Since S and W are perpendicular to each other (one is due south and the other is due west), $\triangle SWT$ forms a right triangle. We can find $SW$ (the distance between the two people) using the Pythagorean theorem: $SW^2 = ST^2 + WT^2 = 5^2 + (5\sqrt{3})^2 = 25 + 75 = 100$ So, $SW = \sqrt{100} = 10$m. Hence, the correct answer is 10 meters, which corresponds to Option A.