Low mood can be a symptom of low testosterone, but low mood can be because of many, many other things as well, not necessarily hormone related. Since you are 51, it's quite possible that you are on the lower end of spectrum. Nobody here will give you a definite answer and probably no one will recommend that you jump on the TRT hoping it will be the magic bullet.
Perhaps, think about other stuff that may have changed lately - relationships, some particular event, some other health issue manifesting itself; there could be plenty of reasons for feeling how you are now..
Talk with your GP, if you can, do blood work for hormones, find our what levels you are at. Try to exclude everything else that might be influencing you before you make any commitments.