# Too much roots!

Algebra Level 4

The rationalization of the expression

$\dfrac{1}{\sqrt{5} + \sqrt{2} + 1}$

can be expressed as

$\dfrac{- A\sqrt{10} - B\sqrt{5} + C\sqrt{2} + D}{E},$

where $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ are all positive integers.

Find the minimum value of $$A + B + C + D + E$$.

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