To find the area of the rectangle, we need to multiply the lengths of its sides.
The right side of the rectangle is given as \(3x^3\) and the bottom side is given as \(-4x^3 + 5\).
Now, we will calculate the area (A):
\[ A = \text{Right Side} \times \text{Bottom Side} = (3x^3) \times (-4x^3 + 5) \]
To calculate this, we distribute \(3x^3\) to both terms in the expression for the bottom side:
\[ A = 3x^3 \times -4x^3 + 3x^3 \times 5 \]
Calculating each part, we get:
- \(3x^3 \times -4x^3 = -12x^{6}\)
- \(3x^3 \times 5 = 15x^{3}\)
Now, we can combine these results to find the total area:
\[ A = -12x^6 + 15x^3 \]
Therefore, the area of the rectangle is:
\[ \boxed{-12x^6 + 15x^3} \]
This corresponds to the third option in the responses provided.