Solution
= Solution
The circle is
$$
\boxed{|z-5i|=5}.
$$
The direction from its center $c=5i$ to $z_0=15/4$ is
$$
z_0-c=\frac{15}{4}-5i,
\qquad
|z_0-c|=\frac{25}{4},
$$
so the corresponding unit direction is $3/5-4i/5$. Moving a distance five from the center in the two directions gives
$$
z=5i\pm5\left(\frac35-\frac45i\right).
$$
Thus the intersections are
$$
\boxed{z=3+i\quad\text{and}\quad z=-3+9i}.
$$