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 :