Answer
The function is neither even nor odd.
Work Step by Step
$f(x)=5+\sqrt {4-x}$
$f(-x)=5+\sqrt {4+x}$
$f(x)\ne f(-x)$
$-f(x)\ne f(-x)$
Notice that:
$f(3)=5+\sqrt 1=6$ and $f(-3)=5+\sqrt 7$
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