Answer
$C$
Work Step by Step
$\sqrt5(2+\sqrt10)=2\sqrt5+\sqrt 5 \sqrt 10$
$=2\sqrt5+\sqrt {50}$
$=2\sqrt5+\sqrt {25 \cdot 2}$
$=2\sqrt5+5\sqrt {2}$
Hence, the correct answer is $C$.
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