Dell inspirion N5010 automaticallt power off problem

Is it shutting down or is the screen just going dark? Cheapest thing to try is to run it on wall power with no battery, if that does not work, try a new power brick. If that does not fix it, take apart the laptop, clean out all the fans, try it again. If that does not work you probably need to have the motherboard replaced.
 

americanbrian

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Sounds to me that it is likely a thermal problem. The laptop is probably shutting down to protect the CPU from heat death.

Unfortunately the CPU is hideous to access. You must almost completely disassemble the laptop (remove the mobo) to access the fan and heatsink.

The stock TIM they use is terrible and cracks quite easily. Replacement with something like MX-4 is recommended.