Step 1:
The given inequality is
$5x-3 \geq 3x-5$
Adding 3 and -3x on both sides of the inequality.
$=> 5x-3x \geq -5 +3$
$=> 2x \geq -2$
Dividing by positive number 2 on both sides.
$=> \large\frac{2x}{2} \geq \frac{-2}{2}$
$ x \geq -1$
Step 2 :
All number greater than or equal to -1 represent the solution of the given inequality.
The graphical representation on the number line is :