how to show date filter by next 5 months via expose filter in drupal?
What you're wanting is Grouped Filters. It will let you set pre-defined discrete filters for your date.

Under the Views UI for your exposed data filter set Filter type to expose to Grouped Filters. You can set your arbitrary label, set your operator to is between, and Value type to An offset from the current time... in the date fields, you can use a relative PHP strtotime() format to specify a filter between the current date ("now") and 5 months into the future ("+5 month").