The problem asks for the area of a rectangle with a length of $\frac{5}{8}$ foot and a width of $\frac{3}{2}$ feet.

The formula for the area $A$ of a rectangle is:

$A = \text{length} \times \text{width}$

Substituting the given values:

$A = \frac{5}{8} \times \frac{3}{2}$

To multiply fractions, multiply the numerators together and the denominators together:

$A = \frac{5 \times 3}{8 \times 2} = \frac{15}{16}$

So, the area of the rectangle is $\frac{15}{16}$ square feet.

Looking at the answer choices, the correct answer is:

C. $\frac{15}{16}$ square feet.

Would you like any further explanation or have questions about the steps?

Here are some related questions:

1. How do you multiply fractions in general?
2. How do you convert a mixed number into an improper fraction?
3. What is the difference between area and perimeter in geometry?
4. How can you simplify fractions after multiplying them?
5. Can the area of a shape be expressed in units other than square feet?

Tip: When multiplying fractions, remember to simplify the result if possible by dividing both the numerator and denominator by their greatest common divisor.