First, let's simplify the multiplication:

-5 2/5 x 3,125 x (-2/5) = (-27/5) x 3,125 x (-2/5)

Next, multiply the fractions:

(-27/5) x 3,125 x (-2/5) = -625 x 27 x 2 / 25

Now, multiply the numbers:

-625 x 27 x 2 / 25 = -33750

Finally, subtract 32 from -33750:

-33750 - 32 = -33782

Therefore, the result of the expression -5 2/5 x 3,125 x (-2/5) - 32 is -33,782.