Step 1: Understanding the reaction.
When phosphorus pentoxide (P$_4$O$_{10}$) reacts with water, it forms phosphoric acid (H$_3$PO$_4$). The reaction is:
\[
\text{P}_4\text{O}_{10} + 6\text{H}_2\text{O} \rightarrow 4\text{H}_3\text{PO}_4
\]
Step 2: Analyzing the options.
(A) H$_3$P(OH)$_3$: Incorrect, this is not the product of the reaction.
(B) H$_3$PO$_3$: Incorrect, this is phosphorous acid, not phosphoric acid.
(C) H$_3$PO$_4$: Correct — Phosphoric acid is formed from the reaction of P$_4$O$_{10}$ with water.
(D) H$_4$P(OH)$_3$: Incorrect, this is not a valid product of the reaction.
Step 3: Conclusion.
The correct answer is (C) H$_3$PO$_4$.