An algebra problem by Sambhrant Sachan

Algebra Level pending

$\dfrac1{\sqrt{4x+1}} \left[ \dfrac{(1+4\sqrt{x+1})^n}{2^n} - \dfrac{(1-4\sqrt{x+1})^n}{2^n} \right ] \\ = \\ a_0 + a_1 x + a_2 x^2 + \cdots + a_5 x^5$

Find the value of $$n$$ that satisfy the equation above.

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