The weight helps me too. But practice certainly goes a long way.
Between range sessions I practiced drawing and dry-firing the pistol until it was second nature- this also really helped break in the trigger.
I should add that I have put 1700 rounds through it, but I'm still not very accurate with this pistol without the weight.- But accurate enough that I trust it as my carry piece.
I dont know if you can do this with the 5-7 but I have helped people with this issue with other guns. Balance a coin on the slide by or on top of the front sight/barrel end. Practice dry firing in a normally aimed manner and this will cure any flinching or jerk you have once you keep the coin balanced throughout the trigger squeeze.