Here, i checked if your current PC is okay with running this game:
http://www.game-debate.com/games/index.php?g_id=651&game=iRacing&p_make=Intel&p_deriv=Core+i3-540+3.06GHz&gc_make=ATI&gc_deriv=Radeon+HD+5670+1GB+DDR3&ram=3&checkSubmit=#systemrequirements
This test has been made at 1080p. What resolution do you use and what framerates can you achieve?
Your CPU does meet the minimum requirements, but RAM and GPU do not. I would recommend upgrading ram to 2x4GB and a newer graphics card. Current gpu (HD 5670) has a performance rating of 3/10, which is very low, meanwhile iRacing says it needs something with a rating of 5-6 out of 10. You can search for graphics cards within your budget range and if you think you found a good deal, go to game-debate.com and search for your graphics card (exact model) and right there it will say what GD rating does it have.
For example, here is your GPU and CPU:
http://www.game-debate.com/hardware/?gid=416&graphics=Radeon%20HD%205670%201024MB
http://www.game-debate.com/hardware/index.php?pid=251&cpu=Core%20i3-540%203.06GHz#compareCpuHeader
You can also look at the graphics card's "resolution performance". 10 = Perfect, meanwhile 2-4 - can't be called a decent pick.