Multiplying Mystery Numbers

Logic Level 1

\[ \large{\begin{array}{cccccc} && & & A & B&5 \\ \times && & & & &5\\ \hline & & & & D & B&5\\ \hline \end{array}} \]

Let \(A,B\) and \(D\) be distinct digits that satisfy the cryptogram above.

Find the minimum value of \(A+B+D + 5\).

Clarification: Both \(A\) and \(D\) are a leading digit, so neither can be zero.

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