Gather Toward the Larger

In $5-x < 2x-4$, the x-terms are $-x$ on the left and $2x$ on the right. Collect them on the side with the larger coefficient. Here that is the right side, because 2 is larger than -1. Then the coefficient stays positive and you never need to flip the sign. Add $x$ to both sides:

$$5 < 3x-4$$

$$9 < 3x$$

$$3 < x$$

The last line says that 3 is less than $x$. Written with $x$ first, it is $x > 3$.

You could collect the x-terms on the left instead. Subtracting $2x$ from both sides and then subtracting 5 gives $-3x < -9$. Dividing by -3 and flipping the sign gives $x > 3$ again. Both ways give the same answer. Collecting toward the larger coefficient avoids the division by a negative number.