Equal Representation

Consider the following formula:

ABCDE
+BCDE
+ CDE
+  DE
+   E
-----
FGHIJ

Where each letter represents a unique decimal digit, and there are no leading zeroes for any number in the formula.

If \(A + B + C + D + E\) is minimal, what is the number \(\overline{ABCDEFGHIJ}\)?
(The string of digits, not the product.)

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