OK So looks like a Shimano Tourney rear derailleur, which has a steel lower cage and isn`t likely to get ripped in half like that just by a simple chain misalignment.

But I`ll repeat - if the bike is really only 5 months old - it should be a warranty issue. If you simply bought it used 5 months ago there is no possibility of knowing the history of that RD.

The other bad news is that unless you replace that chain thats been seriously twisted - you stand a good chance of looking at another new rear derailleur a lot sooner than you might like.