Step 1: The distance between two parallel tangents of a circle is twice the radius.
\[
\text{Distance between tangents} = 2r
\]
Step 2: Given that the distance is 10 cm:
\[
2r = 10
\]
Step 3: Solving for \( r \):
\[
r = 5 \, \text{cm}
\]
Thus, the correct answer is \( \boxed{5 \, \text{cm}} \).