Whenever I read something like this one thing comes to mind....
You need more practice.
And that opinion is based on experiance.
One season in Wyoming (when I lived there) every Deer or Antelope took two shots to finish off. First year with a new to me rifle.
I was so disgusted with myself I swore I would not hunt the next year if I couldn't shoot better.
I practiced. And I adjusted my scope. And I practiced. And I shot a couple of hundred rounds over the course of the year.
Never again did any animal suffer at my hand. And many friends asked to hunt with me knowing they would get their meat in the freezer.
Practice. And know your target.
A hole and blood does not mean a kill.
Incidentally, I have a sawed off double barrel 12 gauge. 18 1/4" barrels.
It develops a good pattern at 25-30 yards. Closer and the shot hasn't opened up. That is due to the plastic wads.
So at 5 feet, your load hadn't begun to blossom.
Go out and spend a few shells getting familiar with your shotgun.
Practice makes perfect.