A five digit number n= a b c d e is such that when divided...

$$\begin{aligned} & \because a \in\{0,1\}, b \in\{0,1,2\}, c \in\{0,1,2,3\}, d \in\{0, \\ & 1,2,3,4\}, \quad e \in\{0,1,2,3,4,5\} \end{aligned}$$ $\because n$ is a five digit number, so $a=1$ and $n$ must be odd. When $n$ is divided by 5 the remainder is $e$ or $e-5$. So either $d=e$ or $(d, e)=(0,5)$ (i) When $d=e$ then $(d, e)=(1,1)$ or $(3,3)$

de	c (divisible by 4)	b (divisible by 3)
11	3	0,1,2
33	1	Not possible

So $n=10311$ or 11311 or 12311 Out of which $n=11311$ is correct when we check the condition of divided by 6 . (ii) When $(d, e)=(0,5)$ then $c=1, b$ is not possible. So $n=11311$