I'm gonna guess you have a common wire issue. Are Zone 3 and 5 near each other - like the common goes from 3 to 5 without going to zone 4?
It is probably worth it to go buy some wire. Disconnect the common at your controller and run a piece of wire from from that common terminal to the common on your solenoid. Turn on that zone and see what happens. If you still have the problem, put your original common back together and run a wire straight from the controller (Zone 3 terminal) to the hot wire on your solenoid. If either of these solves your issue, then you have an intermittent short somewhere. At that point you can try to check your wires at any place you might think you have gotten a nick in the wire. Or, you can run new wire from your controller to the valve. Or, hire an irrigation company with a wire/fault locator to find the bad spot.
If the wire above ground fixes your problem, start with checking all your wire connections - common from zone 2 to 3, etc.
If the direct wire doesn't fix your issue, then you have to have a valve issue or something in your line, but I am betting on a bad wire somewhere.