To find the lateral area of a cylinder, we use the formula: Lateral Area = height x circumference of the base.
First, we need to find the circumference of the base (which is a circle) using the formula: circumference = π x diameter.
Given that the diameter of the base is 5 inches, the circumference is: π x 5 = 3.14 x 5 = 15.7 inches.
Now, we can find the lateral area by multiplying the height (7.5 inches) by the circumference of the base (15.7 inches): 7.5 x 15.7 = 117.75 square inches.
Rounded to the nearest tenth, the lateral area of the cylinder is 117.8 square inches.
Therefore, the correct answer is option C: 117.8 square inches.