Question 735008
EDITED: Correction was needed because of miscalculating and mistating the range.

The domain is all real numbers.  The expression on the righthand side has no restrictions necessary for x.  


The expression, x+3 is zero when x=-3 and |x+3| is never negative.  

THIS PART IS WRONG----------------------------------------------------------
The lowest value for f(x) is where x=0, at which value, {{{f(0)=3-5}}}, or {{{f(0)=-2}}}.  The range is {{{f(x)>=-2}}}.
WRONG PART-----------------------------------------------------------------


THIS PART IS CORRECT-----------------------------------------------------
The lowest value for f(x) is where x=-3 which will be {{{f(-3)=abs(0)-5}}} or {{{f(-3)=-5}}}.  The range is therefore {{{f(x)>=-5}}}  
CORRECT PART----------------------------------------------------------


Few days have now passed, and I thought I'd give the visual part.
{{{graph(350,350,-10,10,-10,10,abs(x+3)-5)}}}