If an antiderivative of \(\large x^4 e^x \) is in the form \( e^x\left(Ax^4 - Bx^3 + Cx^2 - Dx + E\right) \), where \(A,B,C,D\) and \(E\) are positive integers, find \(A+B+C+D+E\).

**Notation**: \(e \approx 2.71828\) is the Euler's number.

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