I'm not a "master" at anything, but I am an experienced handgun shooter, instructor, and competitor.
Handgun shooting is all about consistency. Same grip, same sight alignment, same sight picture (sight alignment overlaid on target -- focus on the front sight), and most importantly, good trigger control. Most folks do a good job with everything but trigger control, because it's the hardest part to master. Pad of your finger on the trigger, or maybe, depending on hand and weapon size, the first knuckle. Squeeze straight to the rear with a gentle increase in pressure, so you don't mess-up the sight alignment. Any extra pressure, or spasmodic jerking/slapping, will be transmitted to the frame of the weapon, causing it to move just as the weapon fires. This movement is masked by the recoil, so many folks don't realize they are jerking the trigger, or moving the weapon off target at the last moment. Have you ever miss-counted your shots, and tried to shoot again when the weapon was empty? Did the front sight dip or nosedive? THAT is the result of poor trigger control. When folks see the sights moving around, there is a natural tendency to jerk or grab at the trigger to try to launch the bullet into the center as the sights move past. RESIST this tendency -- you cannot "jerk" shots consistently into the center, or a small group. TRUST that if you squeeze the trigger gently and hold the sights as near to center as you can, the shots will go in a small group in or near to the center of the target.
Dry fire (practice shooting with an empty weapon) can help with trigger control. Dry fire the weapon until you train yourself to squeeze so carefully that the sights do not move when the hammer/striker falls. Then take that skill to the range, and do it with live ammo (usually a little more difficult). Take your time, don't rush. Competition and self-defense shooters have a little saying -- "You can't miss quick enough to win." Only hits count, so get used to taking the time to get good hits; once you've ingrained the fundamentals, you can speed up and the shots will stay near the center.
At 5 yards, a good shot should be able to keep all their hits on a playing card; or, if the sights aren't quite perfectly adjusted, at least cover all five shots in a single group with a playing card. Using a small, bright-colored aiming spot on the target might help you shrink your groups a bit, as it forces you to hold the sights in a smaller zone than just the big gray general center of the silhouette. I use fluorescent green or red 1" stickers for this; they're usually sold in the business supplies area of many stores (they're used as price stickers).
Good luck and good shooting!