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The surface area of the sides of the cake can be found by multiplying the circumference of the cake by its height.
The circumference of the cake can be found using the formula C = 2Ï€r, where r is the radius. So the circumference is 2 * 3.14 * 5 = 31.4 inches.
The surface area of the sides is then 31.4 * 7 = 219.8 square inches.
The surface area of the top of the cake can be found by using the formula A = πr^2, where r is the radius. So the area of the top is 3.14 * 5^2 = 78.5 square inches.
Therefore, the total surface area of the sides and top is 219.8 + 78.5 = 298.3 square inches. Rounded to the nearest tenth, the baker will need 298.3 square inches of icing.