Suppose \(m\) and \(n\) are two integers, not necessarily distinct, from the set \(\{1,2,3,...,800\}\).

What is the probability that the unit digit of \(2^m+7^n\) is \(5\) ?

If the probability can be expressed as \(\dfrac{A}{B}\) for co-prime positive integers \(A\) and \(B\), submit the value of \(A+B\) as your answer.

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