Answer:
[tex]\boxed{x=0}[/tex]
Step-by-step explanation:
[tex]|x-5|=|x+5|[/tex]
Solve absolute value.
There are two possibilities.
First possibility:
[tex]x-5=x+5\\0=10[/tex]
No solution.
Second possibility:
[tex]x-5=-(x + 5)\\x-5=-x-5\\2x=0\\x=0[/tex]