The iGPU does support DirectX 11 although it may need a driver to do so (doesn't really work well when you install windows, but not the Intel software). But most DirectX 11 games are demanding, and will probably need more then your i5's GPU to cut it. You should check out the system requirements on the game first.
I am having a 3rd generation intel core i5 processor with 4 GB RAM
running windows 7 32bit
I found that Intel core i5 supports Directx 11.0
But when I installed high end games, errors came regarding no directx 11 support...
Does this mean I have to get a graphic card with directx 11 ?
Then why is intel core i5 told to be directx 11 supporting?
For a "high end" game, you will need a separate video card. List your full system specs, model/brand, case size, power supply wattage and we'll be able to suggest a video card (start at about $80 and up to over $300 so also list your budget if you want to play games).