i think because more than 5 years, your imac connection and soldered are cracked, weak,or loose.
if you have much time , you can disassemble the logic board clean it up with 99% alcohol or thinner. it's fine as long as not to clean the plastic materials.
take the heatsinks out and clean them
change the heatsink paste, better give the logic board heat before. about 100c to 150 c (or you can see the capacitors max degree can hold and set it 20% below that) for about 3-5 minutes max. you can look up youtube how to bake logic board. cool it down then go on change the paste.
if you have hot blower, you can focusing the heat at 135c on gpu and cpu for about 2-3 min ( you can also search for references for reflow gpu temperature profile for more details)
put them back together and hope it work.
May best luck with you..
note :
take it with your own risk
careful with it by doing it slowly. take your time
read the references before doing it make your strategy to do the efficient way and not forgetting something.. if it is hard for you to do that then don't waste your time.
i gave you this advise because of my experiences with some mac or pc no matter model.
sometime it did not work. but my worked score still higher...
cheers