It's likely the LCD cable if it's dead, or the PCB. You can swap the cable out but you'll probably need to either get a donor camera, or a used part unless you find a new one that left the supply chain. Nikon is like Apple and goes out of their way to make parts unavailable for users, even when it's just an excuse not to sell them. The PCB is the worse repair of the two since Nikon splits the PCB up with one that has 3 soldered connections plus it's on the frame so you need to replace the LCD frame or assembly as a unit to do it.
Refer to the D5000 guide to remove the LCD so you can swap it: [guide|25250]
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Maybe RtR will change the parts snafu Nikon is known for, but maybe not. One of the reasons I detest Nikon is this parts availability was ruined to sell more cameras and push their service network. Canon has done similar stunts but at least I can buy a screen for an 80D on the open market. Canon may not help me repair the 80D, but I can at least buy it and see what needs to happen.
It's likely the LCD cable if it's dead, or the PCB. You can swap the cable out but you'll probably need to either get a donor camera, or a used part unless you find a new one that left the supply chain. Nikon is like Apple and goes out of their way to make parts unavailable for users, even when it's just an excuse not to sell them. The PCB is the worse repair of the two since Nikon splits the PCB up with one that has 3 soldered connections plus it's on the frame so you need to replace the LCD frame or assembly as a unit to do it.
Refer to the D5000 guide to remove the LCD so you can swap it: [guide|25250]