I have a s5520sc mainboard.
I know that boards before z97 cannot support nvme pci-e m.2 ssd.
after inserting pci-e card for nvme pci-e m.2 ssd,
Can this board(s5520sc) support nvme pci-e m.2 ssd to boot.
Is there a bios hotfix for this problem?
No, not a chance. You need minimum 8 series chipset plus NVMe support in the BIOS. This board was discontinued long, long before the concept of NVMe ever existed and no feature updates happen after board is discontinued.
Thanks for your answer.
Then, Can I use pci-e m.2 ssd by data disk using pci-e card for nvme pci-e m.2 ssd?
I have a multi support(one for nvme m.2 ssd, one for sata m.2 ssd) pci-e card and use it one sata-m.2-ssd.
So, I want to attach nvme m.2 ssd to it and to use by data-disk.
I believe that the answer is no. The issue is that your board supports only PCIe 2.0 and PCIe 3.0 is a stated requisite for NVMe. I believe that you are getting away with the M.2 SATA SSD because it is really using only the SATA lane (which you provided separately; the PCIe connector is being used for power and not much else).
If, somehow, it did work, booting would still be out of the question, as there's no NVMe support in BIOS, but it would be possible to use it as a data drive (with NVMe driver in Windows). I have heard of folks doing this with 8 Series boards. Again, this only work if it runs with PCIe 2.0, but I don't believe that it can. Who knows? Borrow one from a friend and try it out. It won't damage the card, so all that you'd lose is the time spent trying...