i5 3570 boost clock 3791mhz?

To get the 4 extra turbo bins you need a P67, Z68, or Z77 motherboard. Have seen a MSI Z77 and a ASUS Z77 motherboard that can force all cores to the max single core speed. 3.8 goes up to 4.2 on all four cores with multi-core enhancement. On your ASUS H67 motherboard you can overclock the IGP, or increase the FSB to 103 usually or 105 perhaps for only an extra 100 or 200 mhz.
 
No, I don't have that board and I don't see it in the manual. You will have to search through the BIOS/UEFI until you find something set to 100 or 100.00 and try 103 before trying 105. Much more than that has been known to corrupt the data on a hard drive.

https://images_bios.pugetsystems.com/195888.jpg find the BCLK/PCIE entry, 100.0
This is for a Asus P8H67-M Pro/CSM REV 3.0, but it should be similar to your P8H67M LX