Answer
$f(x)=|x+2|-5$
Work Step by Step
Given the standard function, $
f(x)=|x|
$, the equation of the graph that shifts to the left will have a positive constant added to the $x-$variable. Hence, a shift of $2$ units to the left will have the equation,
\begin{array}{l}\require{cancel}
f(x)=|x+2|
.\end{array}
Given the standard function, $
f(x)=|x+2|
$, the equation of the graph that shifts downward will have a negative constant added to the equation. Hence, a shift of $5$ units downward will have the equation,
\begin{array}{l}\require{cancel}
f(x)=|x+2|-5
.\end{array}
