Don't try to make yourself tired 2

Algebra Level pending

\[\large \color{red}{1\cdot 2 \cdot 3 \cdot 4 \cdot 5} + \color{yellow}{2 \cdot 3 \cdot 4 \cdot 5 \cdot 6} + \color {green}{3 \cdot 4 \cdot 5 \cdot 6 \cdot 7} + \cdots + \color{blue}{(n-4)(n-3)(n-2)(n-1)n} \\ = \color{purple}{(n-3)(n-2)(n-1)n(n+1)}\]

Given the equation above, find \(n\).

If you want more questions, please, check out my other question in Part 1 and Part 3 !

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