Changing tabs programmatically and Listening for tab change event in flutter

i am trying to change tabs programmatically with clicking a button so when i run the code everything is okay i click on the fab button and the tabs changes correctly and you can see the index numbers in debug console too ... until the moment that selected tabs is the last one and in that moment when i click on the button i get an error . that i really don't understand it . and i really don't know what to do.

here is my code:

class MyHome extends StatefulWidget {
  const MyHome({super.key});

  @override
  State<MyHome> createState() => _MyHomeState();
}

class _MyHomeState extends State<MyHome> with SingleTickerProviderStateMixin {
  late TabController _controller;
  int _selectedIndex = 0;

  @override
  void initState() {
    super.initState();
    _controller = TabController(length: 5, vsync: this);

    //listener adding...
    _controller.addListener(() {
      setState(() {
        _selectedIndex = _controller.index;

      });
      print("Selected Index: " + _controller.index.toString());
    });
  }

  @override
  void dispose() {
    _controller.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return DefaultTabController(
      length: 5,
      child: Scaffold(
        floatingActionButton: FloatingActionButton(onPressed: () {
          _controller.animateTo(_selectedIndex += 1);
        }),
        body: NestedScrollView(
            headerSliverBuilder: (context, innerBoxIsScrolled) {
              return [
                SliverAppBar(
                  title: const Text('WELCOME'),
                  floating: true,
                  pinned: true,
                  bottom: TabBar(controller: _controller, tabs: const [
                    Tab(child: Text('Flight')),
                    Tab(child: Text('Train')),
                    Tab(child: Text('Car')),
                    Tab(child: Text('Cycle')),
                    Tab(child: Text('Boat')),
                  ]),
                )
              ];
            },
            body: TabBarView(controller: _controller, children: const [
              Icon(Icons.flight, size: 350),
              Icon(Icons.directions_transit, size: 350),
              Icon(Icons.directions_car, size: 350),
              Icon(Icons.directions_bike, size: 350),
              Icon(Icons.directions_boat, size: 350),
            ])),
      ),
    );
  }
}

There is no distinction in cases where _selectedIndex is equal to last.

floatingActionButton: FloatingActionButton(onPressed: () {
  if (_selectedIndex == 4) {
    _controller.animateTo(_selectedIndex = 0);
  } else {
    _controller.animateTo(_selectedIndex += 1);
  }
}),