A vertical compression implies a reduction in the y-values of the absolute value function. Therefore, the term that we use to accomplish the reduction cannot be attached to the x in the equation. If so, we would end up with a horizontal stretch, not a vertical compression.
Compression implies a reduction, or dividing, so our term will be 1/5. This should be placed outside of the absolute value bars so that the compression affects only the y-values.
Correct answer: B. g(x) = 1/5|x|
Hope this helps! :)