To find the total number of hens in the enclosure, we need to simplify the expression given: \((5^{33})^2 \cdot 5^0\).
First, simplify \((5^{33})^2\): \[ (5^{33})^2 = 5^{33 \cdot 2} = 5^{66} \]
Next, we note that \(5^0 = 1\). Therefore, we now have: \[ 5^{66} \cdot 5^0 = 5^{66} \cdot 1 = 5^{66} \]
Now, we need to compare \(5^{66}\) with the choices:
- \(0\)
- \(5^5\)
- \(5^6\)
- \(5^{30}\)
Clearly, \(5^{66}\) is not equal to any of the values given, and since \(66\) is greater than \(5\), \(6\), and \(30\), it denotes that there are more hens than the numbers in the choices provided.
Thus, the correct answer is none of the above choices, as \(5^{66}\) is not listed. If confined to the given responses, and none match \(5^{66}\), it indicates a potential oversight in the problem statement or answer choices provided.