Five choose six equals zero

Algebra Level 4

Let \(h(x) \) denote a monic \(8^\text{th} \) degree polynomial such that \(h(m) = \dbinom m6 \) for \(m = 6,7,8,\ldots,13\). Find \(h(5) \).

Notation: \( \dbinom mn \) denotes the binomial coefficient, \( \dbinom mn = \dfrac{m!}{n!(m-n)!} \) for non-negative integers \(m\geq n \).

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