Among the following, cyclic species are:
(I) `H_(5)P_(3)O_(10)`
(II) `[B_(3)O_(3)(OH)_(5)]^(2-)`
(III) `H_(5)P_(5)O_(15)`
(IV) `P_(3)N_(3)Cl_(6)`

Options

A. I,III
B. I,III,IV
C. II,III,IV
D. I,II,III,IV

Explanation

To determine which of the given compounds are cyclic species, we will analyze the structures of each compound step by step.

### Step 1: Analyze `H5P3O10`
1. **Count Atoms**: The compound consists of 3 phosphorus (P), 10 oxygen (O), and 5 hydrogen (H) atoms.
2. **Structure**: The phosphorus atoms are connected by oxygen atoms. Each phosphorus atom can form multiple bonds with oxygen, and some oxygens can be shared between phosphorus atoms.
3. **Cyclic Nature**: After constructing the structure, we find that there is no formation of a closed loop or ring. The arrangement does not create a cyclic structure.
4. **Conclusion**: `H5P3O10` is **not cyclic**.

### Step 2: Analyze `[B3O3(OH)5]^(2-)`
1. **Count Atoms**: This compound has 3 boron (B), 3 oxygen (O), and 5 hydroxyl (OH) groups, along with a 2- charge.
2. **Structure**: The boron atoms are arranged in a triangular formation, with oxygen atoms connecting them. The hydroxyl groups are attached to the boron atoms.
3. **Cyclic Nature**: The arrangement of boron and oxygen forms a six-membered ring structure.
4. **Conclusion**: `[B3O3(OH)5]^(2-)` is **cyclic**.

### Step 3: Analyze `H5P5O15`
1. **Count Atoms**: This compound consists of 5 phosphorus (P), 15 oxygen (O), and 5 hydrogen (H) atoms.
2. **Structure**: The phosphorus atoms are connected through oxygen atoms, with some double bonds to oxygen and hydroxyl groups.
3. **Cyclic Nature**: The arrangement allows for the formation of a cyclic structure, resembling a ring.
4. **Conclusion**: `H5P5O15` is **cyclic**.

### Step 4: Analyze `P3N3Cl6`
1. **Count Atoms**: The compound has 3 phosphorus (P), 3 nitrogen (N), and 6 chlorine (Cl) atoms.
2. **Structure**: The phosphorus atoms are connected to nitrogen atoms, and each phosphorus is bonded to two chlorine atoms.
3. **Cyclic Nature**: The arrangement of these atoms forms a six-membered ring structure.
4. **Conclusion**: `P3N3Cl6` is **cyclic**.

### Final Conclusion
After analyzing all four compounds:
- **Cyclic Species**: `[B3O3(OH)5]^(2-)`, `H5P5O15`, and `P3N3Cl6`.
- **Non-Cyclic Species**: `H5P3O10`.

Thus, the cyclic species among the given options are the second, third, and fourth compounds.