Among the options given, the number \( \pi \) is the only irrational number.
- \( \sqrt{25} = 5 \), which is a rational number because it can be expressed as a fraction (e.g., \( \frac{5}{1} \)).
- \( \frac{0}{27} = 0 \), which is also a rational number.
- \( \pi \) is known to be an irrational number, meaning it cannot be expressed as a fraction of two integers.
So, the answer is \( \pi \).