Not Between in these date

you have to use greater than and less than operator for this type of query. As of now, we dont have any operator for this type of operations.

As Deepak said...we dont have any any operator called "not between" write a query using less than oct1 and greater than oct5 u can get related result and display it where you want

I would any day suggest to use a combination of two filters rather than using between of any such related operator. 
You can build a logical expression and then add two filters in it. 

1. Filter 1 - Less than Oct 1
2. Filter 2 - Greater than Oct 5

Use the same rule input as the value for both of these filter. That way, you should be able to filter the data.