To solve this equation, we need to first simplify both sides of the equation.

Starting with the left side:
5 - 2x / 3 = (5 * 3 - 2x) / 3 = (15 - 2x) / 3

Now simplifying the right side:
4x - 1 / -5 = (4x - 1) / -5

Now, we can set the two sides equal to each other and solve for x:

(15 - 2x) / 3 = (4x - 1) / -5

Cross multiply to get rid of the fractions:

-5(15 - 2x) = 3(4x - 1)

Expand and simplify:

-75 + 10x = 12x - 3

Rearrange the equation:

-75 + 3 = 12x - 10x

-72 = 2x

Divide by 2:

x = -36

Therefore, the solution to the equation is x = -36.