The electrical currents flowing through the wires almost certainly have no effect on your health.
That having been said, there are lots of ways electricity can be used which can have significant effects on your health. If the electricity is sparking through the air, it can produce ozone, which is harmful to your lungs. Most equipment produces almost no ozone, but motors with brushes in them can have continuously sparking pieces of metal -- try to ventilate your room in this case. Some electrostatic air cleaners may also produce ozone, or they may not, but clean dust, dirt, and mold from the air, making your breathing easier.
Your five-computer example is most likely to impact your body in mind because of the things computers do rather than the fact that they run on electricity. They probably hum and buzz because of their fans, or if they have hard drives with old, screecy bearings that are wearing out, they can give you quite a headache. If they're all playing video games, you can actually get motion sick just by looking at them. Some people in fact can have epileptic siezures which can be triggered by watching frantic, flashing lights (there aren't many such people, but hey, we're looking for health effects here). Just staring at computer screens for a long time can give you eye fatigue. Sometimes if you put several CRT monitors next to each other (this doesn't happen with LCD screens), the image on one or more of them can be jittery due to the stray fields from the deflection coils of neighboring screens. Looking at a jittery image, particularly trying to read a lot of text on it, can give you a real headache.
If the computers are playing video games, they almost certainly will turn your mind to mush. That's what video games are designed to do. Violent video games in particular may give you nightmares.
(republished on 07/22/06)