my guess is two positions at one end work(aka 1 and 2, or 4 and 5)?
if yes, then 2 of the pickups are wired wrong. (if 1 and 2 work, which are the forward positions, then the middle and bridge pickup are wired wrong, etc.)
the problem is there is a variety of 5way switches that are different. i would guess yours is "import" style. are there 8 lugs in a single row on the back of the switch?
if yes, you probably have an import switch.
best i can do in text is tell you that the middle two lugs are common. this means one goes to the volume pot, and there is probably a little jumper between the two lugs as well.
now there are 3 lugs on either side of those 2 common lugs. one set of 3 will probably run to the tone pot in some fashion or be empty. the other set of 3 lugs is for the pickup lead wires. it sounds like at least one or two of those lugs are empty but shouldnt be, or are wired wrong.
i cant tell you colors of your wires without seeing it, but this is how it should be, with the exception that the tone knob will probably be on the bottom 3 lugs somewhere. 1 would be the neck pickup, 2 the middle, and 3 the bridge
hope this helps, feel free to post a pic of your wiring, etc