I think you are mixed up. GDDR5 is the memory on video cards and the video card itself uses a PCIE slot. GDDR3 is also on video cards and use PCIE Slots. They are all backwards compatible down to PCIE 16x 1.1 if you happen to own a computer from 2005.
You are asking if a video card with GDDR5 PCIE 3.0 card will work in a slot that had a video in it that was GDDR3 and PCIE 2.0. The answer is yes it will work.
The ddr5 of the graphics card is for the card only, so it doesn't matter that your computer uses ddr3. And as already mentioned, the PCIe is backward compatible.
I think you are mixed up. GDDR5 is the memory on video cards and the video card itself uses a PCIE slot. GDDR3 is also on video cards and use PCIE Slots. They are all backwards compatible down to PCIE 16x 1.1 if you happen to own a computer from 2005.
You are asking if a video card with GDDR5 PCIE 3.0 card will work in a slot that had a video in it that was GDDR3 and PCIE 2.0. The answer is yes it will work.