More accurate than you think!!!
That weapon is capable of consistantly hitting a man sized target at 100 yards with a little practice. Not that you'd use it for anything but target practice at that distance; it can be done, and it isn't as hard to do as you might think. Gotta use some Kentucky windage though 'til you learn how it shoots.
My brother had a .38 special Charter Arms 5 shot that looked like yours (2 and a half inch barrel), and I was able to hit a milk jug with it at about 50+ yards back in the day when my eyesight was good.
Used to shoot pistols at long ranges (in old borrow pits) to see what they would do. One time we set up an ironing board at 250-300 yards and were able to hit it using a 9mm Walther P-38.
Most ranges nowadays won't allow 100 yard pistol shooting, and the days of borrow pit shooting are a thing of the past. We had fun while it lasted. Ahhh, to be young again. Plinking was more fun than paper target shooting by far.
Les