Your PC should be able to run the NVIDIA GTX 1080. Open up the PC and read the label on the power supply. What is the total wattage? Is it 500 watts? While the PC is open, do some measuring inside and post the maximum length for a graphics card.
If you decide to go with the 1080 and your PSU is only 500 watts then you should replace it with a 600+ watt PSU as some of the 1080s are high power draw.
HP Photosmart 6520 HP Envy 17", i7-8550u,16GB, 512GB NVMe, 4K screen, Windows 10 x64 Custom PC - Z390, i7-9700K, 32GB, dual 512 GB NVMe, dual 512 SSDs, 2K screen, OC'd to 5 Ghz, NVIDIA 2080TI 11GB