5. Add three digits after 168 to form a six-digit number, so that it can be divisible by $3,4,5$ respectively, and make this number as small as possible. Find this six-digit number.
Let the required six-digit number be $\overline{168 a b c}$.
Since $5 \mid \overline{168 a b c}$, therefore, $c$ can be 0 or 5.
Also, $4 \mid \overline{168 a b c}$, so $\overline{b c}$ is a multiple of 4.
Thus, $c=0$.
To make this six-digit number as small as possible, hence $\overline{b c}=20, b=2$.
And $3 \mid \overline{168 a b c}$, thus,
$$
1+6+8+a+b+c=17+a
$$

is a multiple of 3, $a$ can be $1, 4, 7$.
But to make $\overline{168 a b c}$ as small as possible, then $a=1$.
Therefore, the required six-digit number is 168120.