Bridge 4 solution:
http://steamproxy.net/sharedfiles/filedetails/?id=785174305

and success:
http://steamproxy.net/sharedfiles/filedetails/?id=785174522

Bridge 5 makes no sense - you can't pass a cable through the pillar!

I had the same problem with bridge 4 but I found a possible solution:
http://steamproxy.net/id/latwixx/screenshot/447329129849965637

Bridge 4, move the top connection piece on the first part over to the right by one square. Bridge fails, but after a couple of attempts it passes

bridge 4 failed for me too

Yeah. Bridge 4 doesn't work for me. I checked and it's the exact same.

bridge 4 destroyed

That's because these are tank truck solutions. Some of these aren't possible until you breat the levels with the regular trucks to get an expanded budget. For example, Bridge 7 can be completed up to the truck level with a simplified design on the bottom using mostly wood with a few metal parts where there's more stress.

bridge 7, 16k, wat

Not sure how you have 45k budget on Bridge 1 when all I get is 20k
Also, on bridge 4 I only get 15k.