I tried the Barnes 115 TAC-XPD +Ps, and like .41 cal, above, I wasn't impressed. I compared their accuracy to Speer Gold Dot 124 +P rounds using my Shield 9. The target was a 4"x4" square set at 15 yards.
Using my Shield, I was able to hit the square 18 times in 34 shots with the Gold Dots, for a hit rate of 54%. With the Barnes TAC-XPDs I was able to hit only 5 out of 20 shots, for a hit rate of 25%.
Then, I repeated the comparison with my SIG P320 Compact with its longer 3.9" barrel. Using my P320, I was able to hit the square 11 times in 15 shots with the Gold Dots, for a hit rate of 73%. I hit only 6 times in 15 shots with the TAC-XPDs, for a hit rate of 40%.
Although my testing was just a small-sample experiment, the accuracy results were so heavily in favor of the Gold Dots that I've chosen them as my carry ammo, and I have abandoned any thought of using the TAC-XPDs.
Nevertheless, I suggest you do your own comparison tests and find the SD ammo that YOU shoot best. It's possible that your 5" FS M&P CORE will shoot the TAC-XPDs better than my shorter-barreled pistols.
Good luck and good shooting!