1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 13 cm, 12 cm, and height 5 cm, and the prism length (depth) is 16 cm. 2. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Length of prism}$$ 3. **Calculate the area of the triangular base:** The base is a triangle with base $b=12$ cm and height $h=5$ cm. $$\text{Area} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 12 \times 5 = 30 \text{ cm}^2$$ 4. **Calculate the perimeter of the triangular base:** The sides are 13 cm, 12 cm, and 16 cm (given as the prism length, but the third side of the triangle is 13 cm, 12 cm, and the third side is 13 cm or 16 cm? The problem states 13 cm and 16 cm are slant edges, but the base side is 12 cm, so the triangle sides are 13 cm, 12 cm, and 16 cm. So perimeter $P = 13 + 12 + 16 = 41$ cm. 5. **Calculate the surface area:** $$\text{Surface Area} = 2 \times 30 + 41 \times 16 = 60 + 656 = 716 \text{ cm}^2$$ **Final answer:** The surface area of the triangular prism is $716$ cm$^2$.