elementary set theory - Cardinality of the set ${sum_{i=1}^{infty} {{a_i}over {5^i}}} subset mathbb R$

Cardinality of the set

$$A=\left\{\sum_{i=1}^{\infty} {{a_i}\over {5^i}}:a_i\in\{0,1,2,3,4\}\right\} \subset \mathbb R$$

$A.$ Finite

$B.$ countably infinite.

$C.$ uncountable but does not contain an open interval.

$D.$ contains an open interval.

Now I guess the set would be uncountable because cardinality of each sequence ${\{{a_n\over 5^n}\}}_n$ is countably infinite product of a finite set , namely $\{0,1,2,3,4\}$. So option $C$ or $D$ will be the case . But what about the open interval thing $?$ How to find that out $?$

Thanks for any help.