Since $\frac{S_{25}}{a_{23}}=5$,
it follows that $S_{25}=5a_{23}$,
thus $\frac{25 \times (a_{1}+a_{25})}{2}= \frac{25 \times 2a_{13}}{2}=25a_{13}$,
therefore $\frac{a_{13}}{a_{23}}= \frac{1}{5}$. Similarly, we get $\frac{a_{23}}{a_{33}}= \frac{5}{9}$,
thus $\frac{a_{33}}{a_{43}}= \frac{5+4}{9+4}= \frac{9}{13}$,
and $\frac{S_{65}}{a_{43}}= \frac{65a_{33}}{a_{43}}=45$,
hence the answer is: $\boxed{C}$.
Firstly, based on the properties of an arithmetic sequence and the sum formula, we obtain $\frac{a_{13}}{a_{23}}= \frac{1}{5}$ and $\frac{a_{23}}{a_{33}}= \frac{5}{9}$. Then, using the theorem of combined ratio, we find $\frac{a_{33}}{a_{43}}= \frac{5+4}{9+4}= \frac{9}{13}$, and proceed to solve.
This question primarily examines the properties of arithmetic sequences and the knowledge of summing an arithmetic sequence, and is considered a medium-level problem.