Vlookup between two ranges

The attached file has some zip codes that I want to identify the state for.

I want to do a Vlookup into column G that will give me the state for the zip code in question if it is between the zips in Columns D and E. I can't get the formula to work. It would be something like this.

Place the value from Column C into Column G if Column F is between or equal to the values in Column D and E.

Did I explain myself correctly? If any further information is needed please let me know.

Thank you so much in advance for your help.

Eddie.