You can try adding the following conditional formatting:
Condition: DueDate [Is less than] (Use a formula...) addDays(today(), 10)
Formatting: Shade box orange
Condition: DueDate [Is less than] (Use a formula...) addDays(today(), 15)
Formatting: Shade box yellow
Formatting rules are applied in the order they are listed and the first one that passes its condition is the one that will be used, so you'll need to think about which ones need to override others and list them first.