To determine the volume of a round bale of hay, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given the height \( h = 5 \) ft and the diameter of the bale is \( 4 \) ft, we can find the radius \( r \):
\[ r = \frac{\text{diameter}}{2} = \frac{4 \text{ ft}}{2} = 2 \text{ ft} \]
Now, we can substitute the values of \( r \) and \( h \) into the volume formula:
\[ V = \pi (2 \text{ ft})^2 (5 \text{ ft}) \]
Calculating \( (2 \text{ ft})^2 \):
\[ (2 \text{ ft})^2 = 4 \text{ ft}^2 \]
Now substitute that back into the volume equation:
\[ V = \pi (4 \text{ ft}^2) (5 \text{ ft}) = 20\pi \text{ ft}^3 \]
Thus, the volume of the round bale of hay is:
\[ \boxed{20\pi \text{ ft}^3} \]