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.