I agree with what was written, but I think the paintover can demonstrate it better. It's not enough that the head bobs, the whole body bobs. I've exaggerated everything to make the point more clear, although leg keyframes would have to be redone to incorporate this.
The arm movement itself I think it's actually quite fine, smooth, with a nice swing to it. The problem is much more in the legs. Your frame 1 and 5 were the same and the rest of keyframes are not combined correctly. When legs are in the inverted V shape they should be mostly straight and as far apart as possible. After that the feet should come closer. In your case the leg farthest back is not when it's on the ground, but one frame after when it's already up in the air. I can only see that happening while running since you have some time when you're completely in the air. Just look up some walking references to study keyframes more closely.
EDIT: I offset leg positions by one frame so the arm extremes match leg extremes more closely, but really what it needs is complete reworking of the legs to match up with the pacing of the arms. If they are lively like that, the legs need to pick up some of that pace as well.
