Combinatorial Madness!

\[\large \displaystyle \sum_{a+b+c+d+e=15} abcde \]

Given that \(a,b,c,d,e\) are positive integers satisfying \(a+b+c+d+e=15\), find the value of the above expression, where the sum is taken over all satisfying ordered quintuplets \((a,b,c,d,e)\).

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