Multi conditional formatting based on dates

Question

I need to format columns D, F, G, H, & I based on a date entered into column C Formatting needs to highlight any cell in those columns that are blank.

Column D needs to highlight based on Column C +5-29 days.

Column F, H, & I highlight based on Column C +30, +60, +90 days respectively

Column G highlight based on Column C +31-60 days

Once a date is entered into a cell in those columns I need the formatting to clear.

Any help would be greatly appreciated.