Which affects acidity more, in relation to induction? (Distance vs. quantity) I already know that the answer is III. I'm just looking for further explanation on how the others compare to each other, mainly IV vs V. 
I know that iodine is less electronegative than chlorine, making I the least acidic. 
Only having one chlorine atom, while the rest have two, puts II next in line. 
III is the most acidic, due to the two chlorine atoms being on the same carbon, and closest to the sulfur group.

My question comes in for the comparison of IV and V. While V has two chlorine atoms on the same carbon, they are both 3 carbons away from the sulfur group. Meanwhile, IV has one chlorine atom closer to the sulfur group, but the other isn't on the same carbon atom. 
Which one of these is more effected by induction? Proximity to the sulfur group (IV) or being grouped together on a single carbon (V)?
Inductive effects decrease strongly with increasing distance. Thus, the further away an inductively acting group is, the lower its influence will be. For practical intents and purposes, the otherwise very comprehensive Brodwell $\mathrm{p}K_\mathrm{a}$ database does not even list any &#x3b2;-halo compounds; only the difference between &#x3b1;-hydrogen, carbon and halogen is typically given.

Thus, we can expect compound IV to have practically the same acidity as compound II, and that compound V’s acidity is comparable to the unhalogenated pentan-4-thiol. Considering that all chlorines are very far away from the acidic proton, the effects would be smaller still.