For $a \neq 0$ and $b \neq 0$, if the real valued function $f(x)=\frac{\sqrt[5]{a(625+x)}-5}{\sqrt[4]{625+b x}-5}$ is continuous at $x=0$, then $f(0)=$

• A

  $\frac{4 b}{5}$
• B

  $\frac{5 b}{4}$
• C

  $\frac{5}{4 b}$
• Correct answer
  D

  $\frac{4}{5 b}$

Hence, the correct answer is option: 'D'.