Calling sleep(5); and updating text field not working

This will probably provide the result that you seek:

-(void)textLabelChanger:(id)sender
{
    NSString *myTextLabelString = [NSString stringWithFormat:@"%d", gameCountDown];    
    textLabel.text=myTextLabelString;

    [self performSelector:@selector(updateTextLabelWithString:) withObject:@"sleep 5 worked" afterDelay:5.0];
    [self performSelector:@selector(updateTextLabelWithString:) withObject:@"sleep 5 worked second time round" afterDelay:10.0];
}

-(void)updateTextLabelWithString:(NSString*)theString
{
    textLabel.text=theString;
}

There are plenty of ways to do this. Instead of having a single updateTextLabelWithString that you call twice with different delays, you could have a doFirstTextUpdate that writes the “sleep 5 worked” and then calls another selector like doSecondTextUpdate using the same [self performSelector:] technique after another 5 second delay.

It’s exceedingly rare that you’ll need to use the sleep() method with Objective-C.

-(void)textLabelChanger:(id)sender
{
    NSString *myTextLabelString = [NSString stringWithFormat:@"%d", gameCountDown];    
    textLabel.text=myTextLabelString;

    [self performSelector:@selector(firstUpdate) withObject:nil afterDelay:5.0];
}
-(void)firstUpdate
{
    textLabel.text = @"sleep 5 worked";
    [self performSelector:@selector(secondUpdate) withObject:nil afterDelay:5.0];
}
-(void)secondUpdate
{
    textLabel.text = @"sleep 5 worked second time round";
}