How to Remove All Previous Fragments from Current Fragment except current one and first one?

On destroy of the Fragment F5 clear Back Stack upto F2.

Try something like this:

public method in your MainActivity:

public void clearBackStackInclusive(String tag) {
     getSupportFragmentManager().popBackStack(tag, FragmentManager.POP_BACK_STACK_INCLUSIVE);
}

now in your F5 fragment:

@Override
public void onDestroy() {
   super.onDestroy();
   ((MainActivity)getActivity()).clearBackStackInclusive("tag"); // tag (addToBackStack tag) should be the same which was used while transacting the F2 fragment
}

Reference

You can manage tasks with flags. For example, this will clear all the activities on top of home.

Intent intent = new Intent(getApplicationContext(), Home.class);
intent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
startActivity(intent)

So if you start 4 or 5 or more tasks over the Home Activity, you can call finish on the fifth and get back home.

I am looking forward for a fragment version of it, but it depends on the way you manage tasks.

EDIT

I found it for fragments :

FragmentManager.popBackStack(String name, FragmentManager.POP_BACK_STACK_INCLUSIVE)

Which will pop all states up to the named one.