actually, u had to check this one on your own, as u're the one who had the PC
Just measure the case size
also remember that non-Low profile GPU usually are 2-slot width (it's their thickness)
my 2 cents:
i don't think it would fit, low profile cards are made for a reason
for the will it work:
seeing that ur CPU should be around 2nd / 3rd gen, the latest BIOS should support a new gen GPU, so that should be fine
as long ur PC had the PCIe 16x slot and enough juice on the PSU, it'll work (recommended at least 300w for a GTX 1050 Ti)