A rectangular prism has a top face area of 56 cm2, length 8 cm, and height 5 cm. Find W and the total surface area.

Its area is given as $56 \text{ cm}^2$. The dimensions of this face are length $8 \text{ cm}$ and width $W \text{ cm}$.
The formula for the area of a rectangle is length $\times$ width.

$$8 \text{ cm} \times W \text{ cm} = 56 \text{ cm}^2$$

$$8W = 56$$ $$W = \frac{56}{8}$$ $$W = 7 \text{ cm}$$

The value of W is $\boxed{\text{7 cm}}$.

Length $(L) = 8 \text{ cm}$
Width $(W) = 7 \text{ cm}$ (from part a)
Height $(H) = 5 \text{ cm}$
The formula for the total surface area (TSA) of a rectangular prism is:

$$TSA = 2(LW + LH + WH)$$

$$TSA = 2((8 \text{ cm})(7 \text{ cm}) + (8 \text{ cm})(5 \text{ cm}) + (7 \text{ cm})(5 \text{ cm}))$$ $$TSA = 2(56 \text{ cm}^2 + 40 \text{ cm}^2 + 35 \text{ cm}^2)$$

$$TSA = 2(131 \text{ cm}^2)$$ $$TSA = 262 \text{ cm}^2$$

The total surface area is $\boxed{\text{262 cm}^2}$.