Yes, you can. Though I would advise you to make sure your PCI-E1.0 slot is at least a x8 slot, as any graphics card will be bottlenecked at a speed of 4x. If your slot is 8x, make sure you do not put anything above the HD5770/GTX260 inside of it, as you will see reduced performance.
A full length pci-e slot has always been 16x.. 8x measure was for AGP slots.. As to answer the question, it's a YES.. The whole pci-e 2.0 interface idea is backwqard compatible.. Thus, you may place any pci-e 2.0 compatible card in a pci-e 16x slot and/or any pci-e compatible card in a pci-e 2.0 slot.. This even holds true for devices such as sound cards, raid cards etc which due to their pci-e compatible interface can be put on any pci-e slot..