The correct answer is $\boxed{4671}$.
The sequence is a simple alternating subtraction of $582$ and $424$, starting with $5824$.
Therefore, the missing term is $5824 - 582 = \boxed{4671}$.
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The correct answer is $\boxed{4671}$.
The sequence is a simple alternating subtraction of $582$ and $424$, starting with $5824$.
Therefore, the missing term is $5824 - 582 = \boxed{4671}$.