It is given,

electric potential at \( 5 \mathrm{~cm}=V_{1} \)
electric potential at \( 10 \mathrm{~cm}=V_{2} \)
electric potential at \( 15 \mathrm{~cm}=V_{3} \)
We know potential inside a conductor is same everywhere, therefore electric potential at \( 5 \mathrm{~cm} \) and \( 10 \mathrm{~cm} \) distance will be
same, that is, \( V_{1}=V_{2} \)
Now, electric potential is given as
\[
\begin{array}{l}
V=\frac{1}{4 \Pi \varepsilon_{0}} \frac{q}{R} \Rightarrow V \propto \frac{1}{R} \\
\Rightarrow V_{3}>V_{1}=V_{2}
\end{array}
\]
Thus, electric potential at \( 5 \mathrm{~cm}, 10 \mathrm{~cm} \) and \( 15 \mathrm{~cm} \) are
\[
V_{1}=V_{2}>V_{3}
\]