5. Given the equation $a y=b^{2} x^{2}+c$ where $a, b, c \in$ $\{-3,-2, \cdots, 3\}$, and $a, b, c$ are distinct. Among all the curves represented by these equations, the number of different parabolas is $\qquad$.

5. 102.

First, $b^{2}$ has three choices.
Second, if $a^{2}=b^{2}$, then $a$ has two choices, and $c$ has five choices;
if $a^{2} \neq b^{2}$, then $a$ has four choices, and $c$ has six choices.
Therefore, the result is $3(2 \times 5 + 4 \times 6) = 102$.