Delete data after specified time

I have a flutter application. Where I am saving a data in shared_preferences. Now what I want to achieve is that when data is saved it will start a timer for 5 minutes. After 5 minutes the data will be removed and user will be taken to the LoginPage again. This is quite simple. But here the things that I have done again restarts the timer whenever I start the application. I want is that suppose after 2 mins 30 seconds user closes the app. After some time the user again opens the app. Then the app will start from 2 mins 31 seconds and remaining time will be 2 mins 29 seconds. That means the timer will not restart even when the app is opened again.

Future<void> initializePreferences() async {
    final SharedPreferences prefs = await SharedPreferences.getInstance();
    _data = await prefs.getString('myData');
  
    Timer(Duration(minutes: 5), () {
      prefs.remove('myData');
      setState(() {
        _data = null;
      });
      ///navigate to splashscreen
      Navigator.pushNamedAndRemoveUntil(
        context,
        '/',
            (route) => false,
      );
      print("Data is reremoved.");
    });
  }

here the timer starts for 5 mins. The remaining details what I want to achieve is given above. Thanks in advance.

You can listen the app state when app is from foreground (ex: user using the app) to background (user quit the app but not terminated yet).

After listen to app state, you could add another shared_prefs to store the time remain when user pause app, and when app in resume, using shared_prefs previously as argument for the timer method

class _MyScreenState extends State<MyScreen> with WidgetsBindingObserver{}
//add the following inside our initState:
WidgetsBinding.instance.addObserver(this);
//didChangeAppLifecycleState will be:
@override
     void didChangeAppLifecycleState(AppLifecycleState state) {
     super.didChangeAppLifecycleState(state);
      if (state == AppLifecycleState.paused) {
       // went to Background
         }
       if (state == AppLifecycleState.resumed) {
       // came back to Foreground
       }
    }