Solution:

A simplifies to $$x + 7 = 0$$$$x = -7,$$ so it has a solution.

B simplifies to $$|-3x| = -5,$$ which has no solution since absolute value makes everything positive.

Let us make sure that all the other choices have solutions.

C simplifies to $$\sqrt{-x} = 2$$$$-x = 4$$$$x = -4,$$ which is fine.

D simplifies to $$\sqrt{x} = 8$$$$x = 64,$$ which works.

Finally, E simplifies to $$|-3x| = 4$$$$-3x = \pm 4$$$$$$$$x = \pm \dfrac{4}{3},$$ which has a solution as well.

Thus, B is the correct answer.