5. (1998 National High School Competition Question) Let proposition $p$ : The solution sets of the inequalities $a_{1} x^{2}+b_{1} x+c_{1}>0$ and $a_{2} x^{2}+b_{2} x+c_{2}>0$ with respect to $x$ are the same.
Proposition $Q: \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$, then proposition $Q(\quad)$.
A. is a sufficient and necessary condition for proposition $p$
B. is a sufficient but not a necessary condition for proposition $p$
C. is a necessary but not a sufficient condition for proposition $p$
D. is neither a sufficient condition nor a necessary condition for proposition $p$
5. D. From $x^{2}-3 x+2>0$ and $-x^{2}+3 x-2>0$ having different solution sets, we can eliminate $\mathrm{A}$ and $\mathrm{B}$. From $x^{2}+x+1>0$ and $x^{2}+x+3>0$ having the same solution set, we can eliminate $\mathrm{C}$. Therefore, the answer is D.