I know it has been a while since the original post, but I was looking for an answer to this also, and had to keep looking since this thread did not provide an answer that made sense to me though it came up as one of the highest search results. I'll add what I found in case someone else comes here looking for an answer too.
PCI-Express also seen as PCIe or PCI-E is a standard for connecting internal devices to a computer. There are currently (March 2019) 4 versions of the standard, and each of them is backwards compatible. This number refers to the version of programming on the card and the slot on the computer motherboard.
There are 4 sizes to the slots for the cards. x1, x4, x8 & x16. These are known as lanes and a card with a smaller lane number will fit in a slot for a card with a larger lane number. The number of lanes are related to the number of pins on the slot and card. A larger card will not normally fit in the smaller slots, unless the slot is open ended.
Each version of the specification fixes issues with the previous version, but the most significant difference is the increase in bandwidth of each version.
The bandwidth nearly doubles with each version specification
v1.0 - 2.0Gbs per lane
v2.0 - 4.0Gbs per lane
v3.0 - 7.8Gbs per lane
v4.0 - 15.7Gbs per lane
So to answer your original question. If you buy a card that is PCIe 3.0 x16, it will properly fit in a motherboard that has a PCIe x16 slot of any version. The card will be compatible up to the version of programming that the motherboard is spec'd for. You would need to find what version of the standard your motherboard is rated to. In your case that motherboard, Asus P5G41T-MLX3, has one PCIe 2.0 x16 slot and two PCIe 2.0 x1 slots. Since your motherboard has a PCIe 2.0 x16 slot, your PCIe 3.0 x16 card will fit in the slot and it will only run up to version 2.0 of the standard.
Your PCIe 3.0 x16 card could potentially transfer data at a speed of 126.032 Gbs (7.877Gbs x 16 lanes) on a version 3.0 x16 slot. If you run it on a version 2.0 x16 slot the card can only transfer up to 64 Gbs (4Gbs x 16 lanes).
I hope this is helpful to others.