$|-3x|+5=0$ has no solution because absolute values only output nonnegative numbers.
Further:
$(x+7)^2 = 0$ is true for $x = -7$
$\sqrt{-x}-2=0$ is true for $x = -4$
$\sqrt{x}-8=0$ is true for $x = 64$
$|-3x|-4=0$ is true for $x = \frac{4}{3}, -\frac{4}{3}$
Therefore, the answer is $\boxed{\mathrm{(B)}}$.