The HD 5770 should run better due to DX11 though. Already for BF3, sites reported the DX11 path running better than the DX10 path at equivalent settings. The HD 5770 is also still supported in the mainline drivers.
I hope the HD 4870 is the official minimum requirement because they didn't have an older AMD GPU to test with. There's a huge gap between the 8800GT and HD 4870, and the latest driver for all AMD's DX10/10.1 GPUs is the 13.9 legacy
I'm not so sure about running "better" -- performance improvements didn't really show up until DirectX 11.2 and Windows 8.1. That wouldn't apply to a Radeon HD 5770 running on Windows 7.
So I gave him the game, installed it. Again for reference, his system is my old system, stock 2.4 GHz Core 2 Quad Q6600 (it's a prebuilt Dell, so overclocking isn't possible), Radeon HD 5770 minutely overclocked to 890 MHz core clock, and 4 GB of DDR2 system RAM.
I first tried running the game with textures and mesh on high, tessellation low, ambient occlusion on SSAO, post process AA high, MSAA off, all other settings on medium, 1440x900 resolution at the default 75 Hz refresh rate. The result was...painful. The first scene with Cassandra interrogating the player had the game hanging every few seconds, for 10 or 15 seconds at a time. Definitely unplayable.
So I tried turning the textures down to medium, and I adjusted the refresh rate to 60 Hz. Muuuuuuch better. The game wasn't hanging left and right, though the occasional hang still happens. The game tends to hang when progressing through the environment, as if it's loading the upcoming area.
So yeah...as I heard it, the "high" texture setting is the maximum detail setting for the textures, the "ultra" and "fade touched" textures just increase the cache size in the graphics memory for textures to reduce pop-in. I was trying to run the game's highest detail textures on 1 GB of RAM and a 128 bit wide memory bus. Even at a low resolution like 1440x900, the game does not take kindly to that.
I do wonder how much of the bottleneck comes down to the CPU. DAI is supposed to be pretty decently multithreaded, to the point that it won't even start on dual core systems. Stock Core 2 CPUs, even quad cores, are extremely long in the tooth at this point.