ABCDE x 4 = EDCBA
ABCDE < 25,000 or ABCDE x 4 would be greater than 99,999 => A = 1 or 2.
If A = 1 then 1BCDE x 4 = EDCB1, this would mean that the units digit in the product of E x 4 is 1, but the units digit of the product of an even number and any other integer must be even => A <> 1 so A = 2.
We now have 2BCDE x 4 = EDCB2.
The units digit of E x 4 must eqaul 2 => E = 3 or 8. E can not = 3 since 2BCDE x 4 > 80,000 so E must be either 8 or 9 => E = 8.
We now have 2BCD8 x 4 = 8DCB2.
B can be only 1. (B Can’t be 2 since A already is and if B is 3 than 23CD8 x 4 will be greater than 90,000 and we already determined that E = 8.)
We now have 21CD8 x 4 = 8DC12.
D can only be 2 or 7 since the product ends in 12 => D8 x 4 ends in 12 (which is only acheived with 2 or 7) and since A = 2 => D = 7.
We now have 21C78 x 4 = 87C12.
The fastest way to get C is probably by trial and error.
C happens to be 9.
21978 x 4 = 87912