1. **Stating the problem:** We have a right triangle with two sides of length 5 m each and an angle of 30° between them. We want to find the length of the third side or verify the triangle's properties. 2. **Understanding the triangle:** Since the triangle has a right angle opposite the 30° angle, the triangle is a right triangle with angles 30°, 60°, and 90°. 3. **Important rule:** In a 30°-60°-90° triangle, the sides are in the ratio $1 : \sqrt{3} : 2$ where the side opposite 30° is the shortest. 4. **Given sides:** Two sides are 5 m each. The side opposite the 30° angle should be half the hypotenuse. 5. **Check if 5 m is the hypotenuse:** If 5 m is the hypotenuse, then the side opposite 30° is $\frac{5}{2} = 2.5$ m. 6. **Calculate the other side:** The side opposite 60° is $2.5 \times \sqrt{3} = 2.5\sqrt{3}$ m. 7. **Verification:** The sides are 2.5 m, $2.5\sqrt{3}$ m, and 5 m, which matches the given sides if the 5 m side is the hypotenuse. **Final answer:** The triangle sides are $2.5$ m, $2.5\sqrt{3}$ m, and $5$ m with the hypotenuse being 5 m.