1. **State the problem:** Find the surface area of a square pyramid with base side length $5$ m and slant height $6$ m. 2. **Formula:** The surface area $A$ of a square pyramid is given by: $$A = B + L$$ where $B$ is the area of the square base and $L$ is the lateral surface area. 3. **Calculate base area $B$:** Since the base is a square with side length $s=5$ m, $$B = s^2 = 5^2 = 25$$ 4. **Calculate lateral surface area $L$:** The lateral surface area is the sum of the areas of the four triangular faces. Each triangle has base $s=5$ m and height equal to the slant height $l=6$ m. Area of one triangle: $$\frac{1}{2} \times s \times l = \frac{1}{2} \times 5 \times 6 = 15$$ Since there are 4 triangles, $$L = 4 \times 15 = 60$$ 5. **Calculate total surface area $A$:** $$A = B + L = 25 + 60 = 85$$ 6. **Final answer:** The surface area of the square pyramid is $85$ square meters.