PC Turns off once a graphics card is installed

So I'm asking this on behalf of someone who is a novice with computers.

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So she bought a used system on eBay for suspiciously cheap. £250 for a AM5 based system. It's a Cyberpower system that has a a620 motherboard (trying to get the exact model). 8500G APU, 16GB single stick 5600mhz DDR5 RAM and 512GB SSD. Inwin 750w PSU.

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So with the PSU as it is. Just the APU installed it works fine. Can use it for hours and do light gaming no problems.

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She then bought a brand new MSI MAG 850w Gold PSU. Once again system works fine. She then got a RTX 3060 ti used on eBay and once the GPU was installed the pc would power up for 2-3 mins and then shut down. Just completely off no blue screens or anything. So she assumed it was the GPU. So returned it and bought a brand new RTX 5060 ti 8GB from Amazon it arrived today and once again after 2 mins then pc shuts down. So she reinstalled the inwin PSU and again 2 mins after power on system shuts down. Only happens with a GPU installed.

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What could this be? Surely it can't be 2 dodgy power supplies right?