Not dropping ice

When you say ices up do you mean the line ices up back to the compressor. is water overflowing over sump tray? or is it dumping out drain? If you are not getting water over the evaporator plate then it will frost up the evaporator plat all the way back to the compressor.if the water is dumping into the drain during freeze cycle check the dump valve this will not let sump tray stay full of water. make sure water filter is good as this will not let sump tray stay full fast enough. is water pump pumping water over the evap plate?

Look for a stuck float switch. unit fills with water for 1 minute, then the board "looks" at the float to "see" if there is enough water in the unit to run. If float switch is stuck down, it tells the unit there is not enough water and the unit stays in the fill cycle causing the sump to overflow and send water down the drain constantly. Compressor will not run till the board senses that there is enough water to run.

does it have a float mechanism that senses the water level by any chance

OK you mentioned the ice maker had no cubes or not making cubes, try filling tray with water from tap. Let freeze and if the ice drops into ice bin the ice maker is OK. Most times the ice maker thermostat is at fault (pt. 27 in photo) if not cycling. Read OHM's between both coils and they should be very near to same reading, if not replace water control valve=> 4389177 by applying first 120VAC to see if valve opens. If water goes into ice maker this way or OHMs between the two are nearly the same your Ice Maker=>2198597 Ice Maker Assembly may need replaced. If you would like to rebuild your Ice Maker here are the part Breakdown view=>
GS5SHAXN Ice Maker Replacement Parts

Let me know how your ice or water turns out, Thanks Sea Breeze

when the machine first starts, it begins it's cycle in the harvest mode. If the float switch is stuck, it stays in the fill/ harvest mode. Compressor runs and water circulates but no ice is being made. I'd start looking there. Turn the machine on, let it run for about 3 minutes, they very lightly tap the float switch. If it starts making ice, bingo, theres your problem. Let me know if I can be of any more help.

Check the water control valve on back and bottom of refrigerator. One side is for the dispenser and the other side is for the ice maker. When the ice maker begins a cycle the thermostat inside the ice maker begins to warm the bottom with a heating element to allow the ice to move freely and then dump into the container beside it. As the cycle reaches its final resting place a limit switch is pressed inside the ice maker to refill with water and start the process again. So if the water valve does not open and the tray remains empty and the ice maker will try to cycle again if the thermostat says that it is cold enough again. Check your model number again and I will try to get you some drawings. The number looks good but can't seem to pull it up. Let me know what you see and find. Try filling the tray with tap water and see if it will cycle after freezing. Thanks, Sea Breeze

check and make sure that as it makes ice that no water is spilling over or out of the freeze tray. only a set amount of water comes in to refill resevoir. if you lose water during the freeze cycle the water level gets below the blades of the pump and it will sound like the pump is tearing up.

seems that its low on water or float switch is bad. try to clean float

make sure you dont have water sitting under dishwasher in tray. it can cause pump only to run. If there is water in bottom, look under water valve, there is a float-is it surrounded with water?

That on/off arm...you should be able to move it and it will likely make a small click when the switch goes on or off. That arm controls the ice making. There is also a float, is it working freely? It has a switch too. Ultimately, the water is controlled by a solenoid valve. It may be defective. Many of these units are removable to test the switches with a multimeter. Turn off the water and remove to test. Some parts are available...some parts are by the unit only.