Armor Tier Attack Speed

So I noticed on some Armor Pieces it says -5 tier Attack Speed or other numbers. What does this mean exactly? And how much is to much?

 

Your weapon automatically has a certain attack speed (super slow, very slow, slow, normal, fast, very fast, or super fast). The attack speed identification increases or decreases the speed along these 7 (it can never go slower than super slow or faster than super fast). So, if you had a super fast weapon and -5 attack speed on one of your armor pieces, your weapon would effectively have very slow attack speed. Normally, armor or accessories with -attack speed also give a lot of damage to make up for forcing you to attack slower, while those with +attack speed give less damage than others.
The maximum hits per second for each speed can be found here.