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.