5. The axial cross-section of a wine glass is part of a parabola, whose equation is $x^{2}=2 y(0 \leqslant y<15)$. If a glass ball with a radius of 3 is placed inside the cup, then the distance from the highest point of the ball to the bottom of the cup is . $\qquad$
5. 8 .

Let the center of the glass ball be at $(0, b)$, then the equation of the circle obtained by the axial section is $x^{2}+(y-b)^{2}=9$. Since in the axial section, the circle is internally tangent to the parabola, the system of equations
$$
\left\{\begin{array}{l}
x^{2}=2 y, \\
x^{2}+(y-b)^{2}=9
\end{array}\right.
$$

has two solutions. For $y$, there is only one solution. Eliminating $x$ yields
$$
y^{2}+2(1-b) y+b^{2}-9=0 \text {. }
$$

By $\Delta=0$, solving gives $b=5$. Therefore, the distance from the highest point of the ball to the bottom of the cup is $d=b+r=5+3=8$.