1. **State the problem:** Find the surface area of a square pyramid with base side length $5$ cm and slant height $6$ cm. 2. **Formula:** The surface area $S$ of a square pyramid is given by: $$S = B + L$$ where $B$ is the area of the square base and $L$ is the lateral surface area. 3. **Calculate base area:** Since the base is a square with side length $5$ cm, $$B = 5^2 = 25 \text{ cm}^2$$ 4. **Calculate lateral area:** The lateral area is the sum of the areas of the four triangular faces. Each triangle has base $5$ cm and height equal to the slant height $6$ cm. Area of one triangle: $$\frac{1}{2} \times 5 \times 6 = 15 \text{ cm}^2$$ Since there are 4 triangles: $$L = 4 \times 15 = 60 \text{ cm}^2$$ 5. **Calculate total surface area:** $$S = B + L = 25 + 60 = 85 \text{ cm}^2$$ **Final answer:** The surface area of the square pyramid is $85$ cm².