Soreness after say, two rounds of trap or skeet would most likely find fit the culprit.
Soreness after a mere 5 rounds is almost certainly technique.
Some suggestions.....
First, square up behind the gun. With your left foot advanced (assuming you shoot RH) as it you were walking to the target, mount the gun with your weight more on the leading foot. Get behind the gun, not along side it in the classic rifleman's stance. This allows your spine to act as a spring and absorb some of the energy.
Raise your strong side elbow to about 45 degrees. This opens up the "Cup" inside your shoulder joint proper and seats the butt where it can best be employed.
Use your firing hand to PULL the weapon firmly into your shoulder. Use your support hand to PUSH the weapon away SLIGHTLY so if your shotgun were made of rubber, it would be stretching a little between the hands. However, do keep the weapon firmly pulled into the shoulder.
Practice this say, 25 mounts at home 3X or more a week and you'll be delighted at the result.
Also, 7/8 12 gauge loads are becoming common for a very good reason. They do what's needed and kick less. I use them for just about everything but waterfowl and defense.
HTH....