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Sorry, guys.
Tzolkin made an error and I didn't check it. The equation has the only solution 10. When we open up moduls, -6 is here but is not within an appropriate interval.

No,
with absolute values
first you need to break everything in intervals
then solve for each interval
if the solution falls within an interval it's valid.

x<-3, x - (x-2) + (x+3) = 5 => x = 0 > -3, so no solution
-3<x<2, x -(x-2) - (x+3) = 5 => x=-6 , no solution
x>2, x + (x-2) - (x+3) = 5 => x = 10, x>2 so 10 is a solution here