Assume the languages:
$$ a) \, L_1 = \{ w \in \{b,c \}^* | \, w \, \text{contains 'bbc' as substring} \} $$ $$ b)\, L_2 = \{ 1^k 0^m 1^m | k,m \in \mathbb{N} \} $$ $$ c)\,L_3 = \{ w \in {0,1}^* | \, w \, \text{is a multiple of 5 (binary system) }\} $$ $$ d)\,L_4 = \{ d^k e^m f^k | k,m \in \mathbb{N}, \, k < m\} $$
$L_1$: Since we could build an NFA which accepts its strings, it's regular.
$L_2$: Using a single stack or PDA, by pushing $0$ to the stack for every $0$ in the string and then poping from the stack for every $1$ (after the $0$s) in the string, we can determine whether the string is in the language if the stack ends up empty. Thus, $L_2$ is context-free.
$L_4$: Same as above, but this time we need $2$ stacks (LBA). Push $0$s in the first stack for every $d$, push $1$s in the second stack for every $e$ and then pop from the two stacks for every $f$. If the first stack ends up empty and second ends up non-empty, then the string belongs to the language. Thus, $L_4$ is context-sensitive.
Are the above conclusions correct? If so, please provide me with a hint for the classification of $L_3$.