Answer
The only solution is $0$.
Work Step by Step
$|2x-5|=|2x+5|$
$2x-5 = 2x+5$ or $2x-5 = -(2x+5)$
Solving first equation,
$2x-5 = 2x+5$
Adding $-2x$ on both sides.
$2x-5-2x = 2x+5-2x$
$-5 = 5$
This is false statement. So, this equation has no solution.
Solving second equation,
$2x-5 = -(2x+5)$
$2x-5 = -2x-5$
Adding $5$ on both sides.
$2x-5+5 = -2x-5+5$
$2x = -2x$
Adding $2x$ on both sides.
$2x +2x = -2x+2x$
$4x = 0$
$x = 0$
The only solution for $|2x-5|=|2x+5|$ is $0$