Step 1: Understand the dissolution process.
When SbF\(_5\) dissolves in BrF\(_3\), it dissociates to form ionic pairs. The SbF\(_5\) acts as a Lewis acid, while BrF\(_3\) can donate a fluoride ion. The result is the formation of [BrF\(_2\)]\(^{+}\) and [SbF\(_6\)]\(^{-}\).
Step 2: Explanation of options.
- Option (A): This is incorrect because SbF\(_5\) and SbF\(_3\) do not form as products.
- Option (B): This option is incorrect as BrF and SbF\(_7\) are not formed.
- Option (C): This is the correct option. The dissolution produces [BrF\(_2\)]\(^{+}\) and [SbF\(_6\)]\(^{-}\).
- Option (D): This is incorrect because [SbF\(_4\)]\(^{+}\) and [BrF\(_4\)]\(^{-}\) are not the products.
Step 3: Conclusion.
The correct products are [BrF\(_2\)]\(^{+}\) and [SbF\(_6\)]\(^{-}\).
Final Answer:
\[
\boxed{[BrF_2]^+ [SbF_6]^-}
\]