There are two possible solutions to an absolute value equation.
For example, the solutions for #|x|=1# are #x=1# and #x=-1#, because the absolute values of #1# and #-1# are both #1#.
The equation #|x-5|=5# splits into to solutions: #x-5=5# and #x-5=-5#. Now, solve for #x# in both of the new equations.
#qquadqquadqquadqquad|x-5|=5#
#" ↙ ↘"#
#color(white){color(black)(
(x-5=5, qquadqquad x-5=-5),
(x=10, qquadqquad x=0)):}#
Those are the two solutions. We can verify them by plugging them into the original equation:
#|x-5|=5#
Check #0#:
#|0-5|=5#
#|-5|=5#
#5=5" "sqrt#
The solution #0# works. Check #10#:
#|10-5|=5#
#|5|=5#
#5=5" "sqrt#
The solution #10# also works, so both solutions are correct. Hope this helps.