Answer
Yes, the ordered pair is a solution.
Work Step by Step
Plug in the given values to the variables to test if they are a solution to the system.
$(5,-3,-2)$
$x+y+z=0$
$5-3-2=0$
$0=0$
$x+2y-3z=5$
$5+2(-3)-3(-2)=5$
$5-6+6=5$
$5=5$
$3x+4y+2z=-1$
$3(5)+4(-3)+2(-2)=-1$
$15-12-4=-1$
$-1=-1$
yes