Without GPU, pc runs absolutely fine and I am currently using it. But with GPU there is problem.
It's rare but there may be issue with the pci-e slot as well. So it's better to get things checked on a pc repair shop if you can not do it by yourself.
Make sure you have correct settings in Bios ie Initial / First display is set to Auto / Pci-e not iGPU. Alternatively you can reset bios by removing and remounting the CMOS battery from motherboard when PC is in power off state and disconnected from the main power supply ( power outlet of house ). Just remove and put the battery after 2-3 minutes and remount the 5600XT. Make sure your monitor cable is connected to the graphic card. Also alternative ports like HDMI/DVI/DP port if if you can of the card.