Will my computer run it well?

[PathToGlory]

Processer: Intel(R) Core(TM) i3 CPU 540 @ 3.07GHz
Ram: 4GB
VideoCard: ATI Radeon HD 5670 1024MB
OS: Windows 7 64-bit

[Rende]

Depends on your monitor resolution, but it should run on low-mid settings

[HienkyakuX]

I'll say mid at most if your lucky. That is comparing it with 2 cards that I have and this list;
http://www.videocardbenchmark.net/high_end_gpus.html

[Ezodagrom]

I'll say mid at most if your lucky. That is comparing it with 2 cards that I have and this list;
http://www.videocardbenchmark.net/high_end_gpus.html
That is a really bad list, for example the Geforce GTX560 Ti is a bit weaker than the Radeon HD6950, while on that list it's shown above the Radeon HD6970.

Another example, the mobile HD6770M is listed really close to the HD5750, even though the HD6770M uses the same core as the weaker HD6670, which is quite a bit below in the list. Not only does the HD6770M uses the same core as the HD6670, it has lower core and memory clocks, so the HD6770M is actually weaker than the HD6670, even though the HD6770M shows up higher in that list.

Anyway, on topic, the OP PC should run the game fine at the default settings (preset 3) depending on the resolution.