My Timer using AngularJS is not working in HTML page

You need to kick off new digest cycle because Angular doesn't know you changed something:

setInterval(function () {
    var d = new Date();
    var seconds = d.getMinutes() * 60 + d.getSeconds();
    var fiveMin = 60 * 2;
    var timeleft = fiveMin - seconds % fiveMin;
    var result = parseInt(timeleft / 60) + ':' + timeleft % 60;
    //console.log(result);
    var timerObj = {
        timer: result
    }
    $scope.timerArray = timerObj;
    console.log("timer...........");
    console.log($scope.timerArray.timer);

    $scope.$apply(); // <--- apply changes to models
}, 500);

Instead of setInterval, use $interval to run digest cycle for you, after function execution completed.

Code

$interval(function () {
    var d = new Date();
    var seconds = d.getMinutes() * 60 + d.getSeconds();
    var fiveMin = 60 * 2;
    var timeleft = fiveMin - seconds % fiveMin;
    var result = parseInt(timeleft / 60) + ':' + timeleft % 60;
    //console.log(result);
    var timerObj = {
        timer: result
    }
    $scope.timerArray = timerObj;
    console.log("timer...........");
    console.log($scope.timerArray.timer);
}, 500)

Edit 1

To call method after interval gets completed you need to call that inside its promise chain, you could restrict you $interval to call it specified amount of time by adding 3rd parameter which will run $interval function that amount of time.

Code

var interval = $interval(function () {
    var d = new Date();
    var seconds = d.getMinutes() * 60 + d.getSeconds();
    var fiveMin = 60 * 2;
    var timeleft = fiveMin - seconds % fiveMin;
    var result = parseInt(timeleft / 60) + ':' + timeleft % 60;
    //console.log(result);
    var timerObj = {
        timer: result
    }
    $scope.timerArray = timerObj;
    console.log("timer...........");
    console.log($scope.timerArray.timer);
}, 500, 10);

interval.then(function(){
    //this code will execute after interval completion
    //you could call any scope method from here
});

Edit 2

If you call your callback function only once then you should not rely on $interval , better you could use $timeout instead $interval, It will run only once.

Code

var timeout = $timeout(function() {
    $scope.statusDetails = [];
    $scope.timeDetails();
    $scope.get_dbStatus();
    $scope.get_sosStatus();
    $scope.get_cepStatus();
    $scope.get_taskStatus();
    $scope.get_mqStatus();
    $scope.get_mrStatus();
    $scope.get_dmStatus();
}, 120000);
timeout.then(function() {
    $scope.repeat()
});

Edit 3

Basically you will need to add one method which will call on the button click using callInterval which will start the $interval & inside that we will maintain intervalPromise variable which will check if interval already exists then it will cancel that it interval & then it will create a new interval

Code

var intervalPromise;

$scope.callInterval = function() {
    if (intervalPromise) //remove interval if already exists
        $interval.cancel(intervalPromise);
    intervalPromise = $interval(function() {
        //..your existing code here
    }, 500);
};