How find this value $\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}=?$ if the $a,b,c,d,e$ is  $a_{1},a_{2},a_{3},a_{4},a_{5}$ a  permutation

and $a_{i}\in[0,9],a_{i}\in N$,such
$$\overline{abcde}=5\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}$$

Find the $\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}$

where $a_{1},a\neq 0$

my idea:
$$\overline{abcde}=a\times 10^4+b\times 10^3+c\times 10^2+d\times 10+e$$
$$5\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}=5a_{1}\times 10^4+5a_{2}\times 10^3+5a_{3}\times 10^2+5a_{2}\times 10+5a_{5}$$
so we must $$a_{1}=1$$
and $e=0$ or $5$

Then  I can't

This problem is creat this :How find this $\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}$

Thank you,maybe this have no solution too?
I wrote a program in Python to check all possibilities. Assuming $a=1$, It puts all the digits in $\overline{abcde}$ in a list and all the digits in $5  \overline{abcde}$ in a list and checks to see if all the digits match. It returned no numbers, therefore there are no solutions. 

Edit: Here is my ugly code:

for b in range(10):
    for c in range(10):
        for d in range(10):
            for e in range(10):
                new_num = str(50000 + 5000*b + 500*c + 50*d + 5*e)
                a_1, a_2, a_3, a_4, a_5 = new_num[0], new_num[1], new_num[2], new_num[3], new_num[4]
                a_1, a_2, a_3, a_4, a_5 = int(a_1), int(a_2), int(a_3), int(a_4), int(a_5)
                if sorted((1, b, c, d, e)) == sorted((a_1, a_2, a_3, a_4, a_5)):
                    print(new_num)       

print("done")
Pick any $a_1$, $a_2$ etc so they are all either $0$ or $1$.
Now let
$$ a=5 a_1, b=5 a_2, c=5 a_3, d=5 a_4, e=5 a_5$$

By repeatedly taking the difference between the left and right side modulo $5$ and factoring out $5$ you get the above answer.

Example:
$$
\overline{50555} = 5 ~\cdot~\overline{10111}$$