VOID LOOP TRICK

I Need my arduino to wait for few time , say ( 60s ) initally and should remain idle without carrying out any task and later should execute the loop for every 5 seconds .

is there any way to do that ?

Quite a few ways.

No need for "tricks"

how

Sixty seconds delay at the end of setup, and a five second delay at the end of loop.

It's not ideal, but it may get you thinking.

If you don't care about power consumption (that is, you don't need sleep/power down), use a state machine:

unsigned long
    timeSketchStart;

const byte pinLed = LED_BUILTIN;

void setup( void )
{
    Serial.begin(9600);
    pinMode( pinLed, OUTPUT );
    Serial.println( F("Sketch starting...") );
    timeSketchStart = millis();
    
}//setup

void loop( void )
{
    ExecuteStateMachine();
    
}//loop

#define INIT_WAIT           0
#define EXEC_NORMALLY       1
void ExecuteStateMachine( void )
{
    static bool
        bLed = false;
    static unsigned long
        timeExecute;
    static byte
        stateESM = INIT_WAIT;
    unsigned long
        timeNow;

    switch( stateESM )
    {
        case    INIT_WAIT:
            if( millis() - timeSketchStart < 60000 )
                return;

            Serial.println( F("Initial delay done. Beginning execution." ) );
            timeExecute = millis();
            stateESM = EXEC_NORMALLY;
            
        break;

        case    EXEC_NORMALLY:
            timeNow = millis();
            if( timeNow - timeExecute < 5000 )
                return;
            timeExecute = timeNow;

            //do whatever needs doing every 5-seconds in here
            //.
            //.
            //.
            
            Serial.println( F("Execute...") );
            
            bLed ^= true;
            digitalWrite( pinLed, (bLed == true)?HIGH:LOW );
            
        break;
        
    }//switch
    
}//ExecuteStateMachine