The motherboard doesn't have anything written. Are there any alternative methods to find which version of PCI-Express my slot supports?
I am looking for an upgrade and I want to add a PCIE gfx card
The support page you linked in the comments doesn't specify the PCIe version number, only the format (x16). Any PCIe graphics card will fit in there (see also this question) as the different PCIe versions are backwards compatible. Looking at the age of the motherboard, this is most likely PCI Express version 1.0 or maybe 1.1.
You can read about the differences between them on this wikipedia article.
Should you decide to upgrade, make sure you check
But to answer the question: check the product's manual. There is no other way to physically deduct the PCI Express version, although some manufacturers might print the version number on the board itself.