Step 1: Identifying peroxy acids.
Peroxy acids are compounds where the oxygen atom is attached to two other oxygen atoms, and they can be formed from sulfuric acid. \( \text{H}_2 \text{SO}_5 \) is the peroxy acid.
Step 2: Conclusion.
The correct peroxy acid is \( \text{H}_2 \text{SO}_5 \), corresponding to option (1).